We have the same regrets about our first house! The RE agent held a silent auction with another couple who didn't even have finance in the end and wasn't putting the figure to the owners each time like he should have. It was also the peak of the market in retrospect.
We know that we definitely can't do the $40k. Another $10k at the most is about it with proviso of an extended settlement to try and cut down on bridging loan fees. ie. can go higher if saving in fees on our end.
Our approval for a higher loan amount is currently in the system. Will know in a couple of days.
On the other side of it all - we don't want to kick ourselves if it only goes $5k above what we have set our limit as!