Oh yhun the sleepless nights really test the gentle parent in me...and I think is this the right thing to do! But you know whats in a few weeks ( I know that seems like ages away) It will settle and it will pass and you will be getting more sleep!
Have you tried co sleeping? My DS1 was a sleeper like your bub and once he came into bed with me we both got way more sleep? Or even use the cot in your room agains t your bed with one side down so bubs isnt in your bed but within reach? And let bubs suckle if he has to...i know it is so uncomfy sometimes but its only for a short time!

your doing a great job and please try to sleep when he does! Good luck xxx