This kind of problems a lot of companies face but obviously there is a solution. Although, it would involve huge amount of patience and dedicated efforts but result is guaranteed.
Intensive use of LinkedIn is the best bet instead of focusing on keywords. A lot of people do use LinkedIn but their experience of generating qualified leads is not that great. I suggest you look for LinkedIn expert/Lead Gen Company who can help you to mine qualified leads which can eventually become your customers.
I am saying this based on my past experience of working with some of the top MNCs across the globe.
Should you need help, feel free to get in touch with me.

It's tough to give specific advice without knowing what industry you're in, but considering that you're targeting an older audience and you're up against some major competition, here are a few things I'd recommend to improve your lead gen:

- Build partnerships. Find other popular products/services in your industry that aren't direct competitors to your company, and start having conversations with them. See if you can agree on a mutually beneficial way of collaborating. Some examples: co-host a webinar or co-author a whitepaper that you both promote, and you both get the leads you generate from it; offer a revenue share for the partner company to promote your product; host an event together and invite both your audiences to attend. These are all great ways to get in front of a wider audience of folks who you know are good targets for your company.

- Mini apps or tools are a great idea, and I'd definitely recommend those as a way to provide additional value to potential leads & customers. You might consider hiring an external developer to build something for you in a shorter time frame if you have the budget. If not, try creating something on your own, like an educational email series or a bunch of video classes.

- Do user testing. Especially when you're going after a non-traditional audience, it's important to get a really strong understanding of who your users are, what their needs and challenges are, and how you can best build your website and product for them. Recruit 4-5 people (ideally folks who would be a match for your target customer) and spend half a day running a 30 min user testing session with each. Have them look at your landing pages and offer feedback. You'll get some really good perspective and suggestions on how to optimize them for higher conversion.

Happy to chat about other ideas if you'd like to hop on a call. Best of luck!

This may be worth pursuing:

"I'm thinking on trying long-tail keywords and building nice looking landing pages to match them, thoughts ?"

It's a strategy I've looked at in some detail from the domain-industry vantage point. Whether it would work for you or not, I can't say without knowing specifics about your business, the competition, prospect customers, and the keyword verticals of interest.

But it's worth evaluating. Even then, much depends on execution. That includes trial and error ... or A/B testing. With the right landing pages, positioned efficiently, it works for some people quite well.

You mention "I'm not sure what will produce the fastest results." This approach isn't the fastest. It's a mid-term or even long-term play.

But you also say, "Competitive keywords don't generate qualified leads and competitors have 3x the money to invest". In that case, maybe a long-term, outside-the-box, experimental strategy would help you find ways to punch above your weight.

You mentioned long-tail in which case I'd recommend reading this article to learn more about how you can use content targeted at long-tail terms to generate organic traffic: http://blog.ispionage.com/400000-organic-visits-from-long-tail-content.html.

I'm not saying that's the best approach for fast results, but if long-tail is something you're looking at, you may learn something from the read. It's also an approach that requires effort and time which creates a barrier of entry to your competitors copying your efforts and doing the exact same thing.

The best way to “produce results faster” is to evaluate your current efforts and determine points of optimization. A/B test your existing messaging to see if you can squeeze more conversions out of your existing leads. Lead generation won’t mean much if you don’t have an effective way to convert those leads.

Long tail keywords are certainly a good place to start. Make sure your messaging on your site supports leads obtained through long tail keywords. If you are targeting an audience that is primed to purchase, you need to keep them primed as they move through your site.

I worked in a niche, enterprise software company for quite some time and ran into a similar dilemma. You're right that you will never win a bidding war against established players. That leaves you with 2 options. 1) Fight them where they are not or 2) Fight them where budget isn't a determining factor.

1) Fight them where they are not
Identify partners that are already providing value to your target audience. Determine how you can provide a joint value proposition with the partner to the customer. Sponsor content on their blogs / websites / events. Arm the partners with all the materials possible so they can generate and convert leads for you.

Leads generated by a trusted partner will greatly shorten your sales cycle. In my experiences, we observed 6+ month cycles without a partner involved and a <1 month cycle with partners involved.

2) Fight them where budget isn't a determining factor.
User groups or meetups are a great way to get in front of niche audiences. Attendees are more qualified than any keyword driven campaign can accomplish. Additionally, these meetups are typically less saturated by bigger players. It is your chance to become the voice of the people, rather than just another vendor.

The same logic applies for online forums. Obviously, forums are a collection of similarly motivated people. Identify the right forums and inject genuine content while engaging in other users’ content. If you have the time and ability to participate you will quickly become a thought leader in the niche. This is one of the lowest budget steps you can take to grow and convert quality leads.

Like I mentioned, I spent a long time in this niche software and spent a long time spinning my wheels. Fortunately I had enough time to experiment and implement strategies that yielded success. Hopefully this advice can help you shortcut the process!

Here is a small marketing tip for you if you want to get quality leads:

Define your Audience: Who is your audience? What is their job title? Which region?

Lets take for example: I want to target HR manager to sell them my HR Platform:

Here are my plan:
Scrap First/Last Name/Company name from LInkedin.
Scrap HR Database (indeed.com, monster) for HR Emails.
Extract Profiles ID of all users who liked a HR Application.
Partner with an HR blog to install my Cookie Remarketing.
------

What you do with all this data?
All the scrapping data which you collected, you will upload it to Adroll, Facebook, Twitter.....
This way, you target all your potential clients. Doing this way, your CPL will cost around 25$ and you will have 300% more revenue.

Old marketing technics don't work, marketing is evolving, so marketing strategies are evolving.

This is just a tip, you will have to research for your self or we can schedule a call and provide more guidance.