Woodnthings suggestion is good. Another option is to make yourself another long square from stable hardwoods and cut off an end to fit into your mortise. I struggled with your delima until I started cutting my mortises with routers... They hold the bit at 90* and a 1/4 or 3/8 bit are exactly the size you choose. My MT joints are now always very near too perfection. I assemble them by hand (no mallet etc. needed) and take them apart by hand, yet the hold when I pick them during dry fit. I can elaborate further if you have any questions.
Its' never hot or cold in New Hampshire... its' always seasonal.