I'll share with you my experience changing aspects of the drivetrain on my '02 Stumpjumper. While I am a "Shimano guy" for several reasons, other manufacturers have offerings that will work well and rather than product endorsement, it should be taken as what I've done. One caveat: mixing brands of drivetrain components, specifically, rear shifters and rear derailleurs, is typically NOT recommended.
The above Stumpy has a 2x10 drivetrain, 34-24 front, 11-36t cassette. Shifters are Shimano SLX 10 speed, with the left being able to switch from 3x to 2x. My gearing ranges from a low of 0.66 to a 3.06 high. Your proposed 1x gearing is 0.8 low 2.90 high in comparison. The broader range is one reason I like 2x. Mountain front derailleurs can be sourced for little of nothing these days, and set-up, shifting and shift patterns is easier than ever. I typically ride the big ring exclusively, but either way there is no chain rub and despite the cross chaining, this isn't such an issue these days with 2x systems and narrower, flexible chains made better with wear and friction reducing materials. Also the large-large cross chaining, which is common with a 2x mountain system is the lesser evil anyway.
Arguably, two things are necessary for a 1x system to function with any degree of acceptable performance: a narrow-wide chainring and a clutched rear derailleur. Due, in part, to the chain guide action of the front derailleur's cage being absent in 1x, chain retention is a necessary consideration for these systems. The narrow wide ring prevents side to side movements of the chain that can lead to derailment. The clutched rear derailleur has a setting that prevents movement of the derailleur cage when the bike encounters bumpy terrain, thus preventing the chain from becoming momentarily slack. As has been pointed out, the RD-M750 lacks this capability. In addition, Shimano trickles down the technology developed at the highest, XTR, level of components to the mid-range line up in fairly quick succession. Thus, today's Deore lineup was yesterday's XT/XTR as evidenced by Deore being 12 speed with Shadow+ design derailleur's initially only offered at the XTR level. Point here is the older XT derailleur, while still decent in quality and performance, won't keep pace with the new Deore. I can attest first hand that the M750, which I owned, failed in an experiment when I was feeling out turning a hardtail into a 1x with a chain guide and 11-40t 9 speed cassette from SunRace. It couldn't climb the chain onto the large cog even with the B-adjust bolt turned around (for maximum length to create maximum distance between the cage's jockey wheel and the cassette's large cog). One could use a goat link or like product to extend this gap, but you'd still lack the clutch and have trouble getting the 11 tooth cog to work.
You could get a 10 speed 2x crankset and maintain much of the range you have with the 3x. A 2x front derailleur is not expensive and your current left, front shifter can still be used as the 2x crankset uses the middle and small ring positions you'd simply toggle between 1 & 2 at the shifter. When your budget allows, turn everything over to 1x11 by getting a narrow-wide chainring of the same BCD as the 2x crankset, a right 11 speed shifter and rear derailleur and 11 speed cassette. Twelve rear cogs may be a problem for two reasons. First it requires a compatible rear hub, meaning a new rear wheel which would arguably be the highest priced single item of a conversion. Second problem may be rear triangle spacing if it is 135mm. I believe I'm correct in saying there isn't enough space there for a twelve speed cassette and anyway you won't easily, if at all, find a 135mm rear hub sporting a microspline or XD driver required by a 12 speed cassette.
Also mentioned by others is the option to buy a 1x11 group set having all the components and new chain necessary to convert. The used market is fairly brisk right now and your current XT derailleur still fetches a price that shouldn't be scoffed at.