Need help resolving a 1903's insufficient headspace

[RossMkIIEnjoyer]

There is a reamer you can get called a pull through finish reamer get that has a rod attached that runs through the end of the barrel I've seen used. Seemed like a relatively simple job. They're not too expensive and can be resold when finished. Cheaper than a gunsmith. Or just a good excuse to get more tools.
This guy uses one at 21:45: