How bad would it be to start sending emails to companies and startups that look interesting asking if they have an opening for someone like me?
I'd take time to customize the pitch and make it obvious that you're sending it to someone who may be or may know a good fit, as opposed to any routable inbox you can find from the Internet.
example one:
Dear sir,
I am a C# Java C++ engineer from $LOCATION with extensive experience in mobile applications, front-ends, ... <-- absolutely nothing in here suggests that they know who I am, and they're imposing on me because they're offering nothing of value to me.
example two:
Hey Patrick!
I've read between the lines of some of your recent posts, and it seems like you are overwhelmed on Appointment Reminder. [Patrick notes: Someone literally wrote this to me last week. Got my attention in a hurry.] I'm an experienced Rails engineer with 6 years of experience working with legacy codebases. I think I could take the engineering work for AR off of your plate, so that you can focus on marketing/sales. Would you like to have a chat about what that could look like? I am open on next Monday and Tuesday from $TIME to $TIME -- what half-hour in there works best for you? <-- Even if I were not interested in this, I'd be interested in this. It is very respectful of my time, demonstrates unique understanding of my situation, etc.
Focus your search on networking with senior execs who you know how to help, ex local CIOs/CTOs.
Don't lead with a resume, instead ask them a question-- do know anyone who needs software development help? Asking for a referral opens up the conversation to more possibilities. It also makes you stand out as a peer, not a supplicant.
I would be worried about sending my personal information that appears on my resume (phone numbers, address, full name) unwarranted to someone. I would start by sending a quick email explaining your skills and maybe a link to a portfolio or github, and ask about openings. If they express interest then I would further pursue. If they don't, all they know you by is your email address.
Where it gets into spam is if you send the same copy & pasted text to dozens of possible employers.
Not sure if it's helpful.