Chillout and enjoy the BBQ! BBQs are fun enough in themselves, very relaxing. Talking shop tends to be frowned upon but I see no problem with it as long as you don't start with it or let it dominate the afternoon. Imho you should not mix friendship with business, ever. Very simple, hire a nondescript tech company or, if you have to, ask him who he would recommend.
Entire thread had me confused until I realised that when you said "Huge cooler master towers" you were talking about Coolermaster tower PC cases... Man I'm slow today
But seriously though, is the rebuilding of two systems into a couple of smaller chassis a major topic of discussion? That's the sort of thing I would just say "that needs done. I'll do it" to, and have it done in a couple of hours. Or have I missed something? Are we talking about systems that are mission critical and have to be on 24/7 or replaced with backups when they are down for maintenance?
Rather than straight-out discussing a business opportunity, I'd tell him you're thinking of this project and ask for his advice, what things you'd need to avoid doing, what you must do, etc. and then if he seems amenable, ask if knows anyone that would do the job properly.
Sounds like an afternoon's work to me to be honest, not nagging at all. I don't see why he would have a problem with you mentioning it to him after dinner, most people would just be glad of the business. Just do what I usually do; "oh by the way, I might have a bit of work that I'd like you to do sometime, could you leave your number and I'll call you about it?". It's as simple as that. So, if I have this right, you run a business from home? Or are these machines you're talking about just the "family PCs" or whatever? Sorry if I'm getting the wrong end of the stick.