Think you are overstating the issues, supply problems cuts both ways. If Rangoon is in British hands they can supply a lot by sea and cut the supply in the East. If Singapore is holding then the Japanese supply losses by sea will be very heavy (subs with working torpedoes based near and only two ports really to interdict, Japanese ASW is poor, think drumbeat levels). Japan just does not have the transports to lose and land supply is basically one railway line.While a successful British offensive out of Burma, into Thailand might cut off the overland supply route, of the Japanese army. The chances of the British being able at this time, to conduct such an offensive, are slim to none. Given the total lack of logistical infrastructure on the Burma Thailand border, such an offensive would require assets that the British do not have. Britain has two principal aims in Burma, at this time, keeping the Japanese out, and the Burma road to China open. And even if the could cut the Japanese overland route, the Japanese will still be able to send supplies by sea, as the RN is not in a position right now to enact a total blockade of the sea route between FIC and Malaya. Yes they can at a high cost to themselves, force the Japanese to pay a high price to maintain such a sea link. But given the far more pressing requirements of defending the area around the DEI, that will be the number one priority for the foreseeable future.