A bit more than your budget, but get a Hummer and never look back 8)

It’s a common problem. Fasten one of the 5mm hex keys in a vice pointing up. Put the wheel on the key. Get a 5mm hex socket adaptor with a Tee handle, apply firm but even pressure, it will give. DO NOT try to jerk it off, Phnarrr! The end caps will burst if you are not carefull. I know from experience. Do not overtighten when you reassemble.

Is the axle shaft flush with the bottom of the recess in the crank arm? If so, the cranks have been over-tightened over time allowing the crank to move too far up the taper. Middleburn will replace these under warranty for a nominal sum, if you contact them.