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.