I had to do cold turkey in the end when I went back to work. DD1 [terrible sleeper, lots of overnight snacking] refused to drink any sort of milk at all for about 6 months. We put into all her food instead and the GP and health visitors were totally unconcerned [she was a bit of a chubster] I was massively stressed though as according to all the manuals, she should still have been getting lots of nutrition via milk, and keeping her hydrated over the hot summer was tricky.
With DD2 things were heading down the same track as her big sister [mix fed from birth, started to drop formula milk feeds rather than BF when being weaned and then became a total bottle refusnik. It all came to a head when she got a nasty cold/cough virus and would only take milk. I simply didn't have the supply and she finally cracked.
In both cases though they were fully weaned from BF by 8.5 months old. Working and bfing did not work for me. DD2 naturally weaned onto formula as I couldn't get home early enough before she was screaming for a bottle of milk and bed.
At 15 months I would be comfortable that my child was getting enough nutrition from solids. I think you are going to have to woman up and tough it out, refuse to feed for the next few nights and deal with the screaming. It is just temper imo. Distraction can help. I could recite The Gruffalo in the dark by the time my DD would sleep through but it was only when I went back to work and she was out and about all day with childcare that she was knackered enough to simply conk and sleep straight through.
BF at bedtime if you want to continue it but then refuse to entertain any more demands until morning. I think that's confusing for a small child though as there isn't a clear message that there is no more food available via boob so if you want to stop feeding, then do.
With some children it works for the partner to resettle / offer the feeds but in my experience [admittedly with younger children] it was counter productive as they just sobbed their hearts out trying to get me into their rooms. Much less stressful all around for me to say no even if I had to do a bit of co-sleeping. If your child is actually thirsty they will take a cup of water.
Is your DH a patient man? If you stayed with a friend on Thursday and Friday night would he be ok to deal with your son overnight. You don't need to have your son still screaming the house down on Sunday night. 2-3 nights usually does it.
The alternative is that you drive into a ditch in the next few weeks and don't see your child grow up. Sorry to be brutal but you need to put this into context if you are really only getting 45 mins at a stretch. It's not sustainable.