I'm working on this post in regard to the sort of conflict between being forced to place a bet (as opposed to the excitement of making a bet when you want to) and a combat system being the only fun of a book. So you have to do combat to have the fun of the book, but that means your forced to make a bet (the 'bet' being gambling your characters life on dice rolls for XP and gold)...and maybe you can see the contradiction.
Anyway I wanted to have some ideas for play with the piece and although I can't think of a bunch, I thought I'd have some posts that include one at a time.
Lumbering - if you do this, you're okay! See, I want to keep with the gamble aspect, so maybe a strength roll DC: 15 and if you fail that, a DC: 15 con check or otherwise you are too tired to do any more lumbering today and you have to make a con check tomorrow to see if you're too tired for it then as well (if that fails you can try the next day without rolling again). If you're using a hand axe, you are at disadvantage on the strength check.
You can make 1 silver for a log at town or 5 copper at a village. Probably up to three a day (perhaps after a week it's just one a day as local demand diminishes)
Gamble aspect: Go to the blacksmith and you can get your axe sharpened by a blacksmith (for 1 silver in town or 5 copper at a village if they have one) - this gives you advantage on the strength check. However, sharpening only lasts for that day (sorry simulationists, this is for game purposes. Please don't argue. It's boring)