Chief. This all sounds very familiar! By just simply sending out CVs or filling in on-line applications it will result in a large collection of PFO letters. You have to make yourself stand out from the crowd. I was in exactly the same boat as you. Wife, 2 kids, mortgage, job etc etc. It was a nightmare. Thing is you have to do something. I’m not saying you won't get a job, but you are the same as countless CLP/IR pilots with 200 odd hours. I could not give up my job to instruct. Same reasons as you. You have to adapt it then. I found a great flying school that would let me work part time. I instructed on my days off. It built my hours, and improved my networking. Getting time off for courses was also difficult. What I sorted at work is that I would work some of my days off, to build days off that I could take all at once. Don't get me wrong, your wife will need to be pretty understand as I was practically a stranger at home sometimes. I would walk in the dog would growl at me, and the kids would ask the wife who the strange man was in the kitchen!
It did make the difference though. It started to narrow down the numbers, I was now in a slightly smaller pool of CPL/IR pilots who instructed. Your networking has to be quality networking, with key objectives. It’s no good just saying "I know Bob, and he’s a pilot at BA". Realistically this would not achieve anything. However, if Bob is best mates with the Chief Pilot at a turboprop airline and is playing golf with him on Tuesday, where they are discussing the pilot turnover at the moment, well there you go. You have to raise your game. If I can give you any steers then please PM me.
It is all a real test of your mental strength and ingenuity. Get it right, and you will secure that elusive position. Remember it's just one lucky break. It might take a few years to get, but that is all you need.
