At the risk of being rude, Raptorduck, I am going to say there are a few things that don’t make sense for me with the things you have posted.
First you say you want to do it right this time but you are shopping now. Yes, you can be more in the drivers seat now than when you were buying the first time but the road isn’t safe.
Now you have mentioned a few times the possibility of “stretching”. This confuses me. Why would anyone who didn’t have to stretch do so? I can see a poor person stretching to get into the most humble house they could afford. Why would some one with your kind of budget choose to stretch?
Stretching and buying in this market is a bad combo IMHO.
Stretching to buy a house sounds so 2005.