Swapping XT hydraulic brake

Currently the CX is a bit of a mongrel, with a flat bar, LH brake is front XT hydraulic disc with RH rear "V" brake.
Coming in this morning on the road bike I was toying with the idea of converting the CX back to drops by putting A TRP HY-RD on the front and mini "V"s on the back. This would seem to work from the box of spares but then I'm left with a LH front XT which is too good to be left in the box of spares.
Is it possible to reconstruct the LH lever to be RH operation and then I'd fit it to the MTB which needs a new front brake, to match the SLX brake I've recently changed on the rear.
To do this I'm assuming that the reservoir would need to be swapped to the other side once it is swapped over, which is the "is this possible" question.
Coming in this morning on the road bike I was toying with the idea of converting the CX back to drops by putting A TRP HY-RD on the front and mini "V"s on the back. This would seem to work from the box of spares but then I'm left with a LH front XT which is too good to be left in the box of spares.
Is it possible to reconstruct the LH lever to be RH operation and then I'd fit it to the MTB which needs a new front brake, to match the SLX brake I've recently changed on the rear.
To do this I'm assuming that the reservoir would need to be swapped to the other side once it is swapped over, which is the "is this possible" question.
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I've already ordered a replacement MTB unit, just have to think about whether I'm going to change the CX over to drops. It does mean losing the MTB STI levers which I really don't want to lose...perhaps when these break then I'll do it.
Everyday Commuter