Frank, i didnt soak anything beforehand
Well, I carved a new wedge, let it sit in linseed oil for three weeks, and today is the first day i got out to use it.
when you say 'let it sit in linseed oil for three weeks', do you mean the entire head in a bucket of linseed oil, wrapped in a rag soaked in it, or just covered in a thick layer of oil? Ideally you shouldn't need more than a few thin coatings of linseed oil, just enough to create a layer of penetrated wood on the outside that helps buffer the exchange of moisture as weather conditions change. It definitely shouldn't be necessary to keep the head soaked in linseed oil for 3 weeks. The only time you should need to soak it even overnight is if your head is loose and you absolutely have to use it the next day but can't make a new wedge/haft in time. If it needs that drastic of measures you should redo the wedge or entire haft, depending on the condition of it.
if you want to salvage the wetterlins handle without going to to much extra effort, I'd suggest mimicking the wedge they have but increasing the thickness slightly. If the wedge came out as made by the factory, it's probably because the surfaces were too slick between the wedge and kerf, there was just enough room for the head to wiggle (possibly caused by dryer conditions shrinking the wood), or because the wedge was improperly formed. An example of how it might be improperly formed is if it bottoms out but the top of the wedge wasn't thick enough completely fill the top of the eye. Or the bottom portion of the haft wasn't big enough enough to fill the eye, and the bottom o the wedge wasn't thick enough to spread the kerf apart enough to fill it.
When all is said and done, the wedge shouldn't be 100% bottomed out because you need to have some room for adjustment later on if you find the head wiggling a bit. You should be able to get it in at least 3/4 of the way in, covering more than 1/2 the heigth of the head. If it's bottomed out, you have to start all over or use metal wedges. Metal wedges are fine, but they are a back up to a properly fitted eye, it shouldn't be necessary. They also make it harder to drill out/rehaft later on. Ideally the bottom of the haft that fits into the eye should be wide enough to wedge itself in without wedge being inserted, and the wedge should be thick enough to fill in the kerf and really apply pressure along it's entire length. If it's short and too thick at the top the only place that has pressure is going to be at the very top of the wedge, which will make it more likely to spit out.
if there are any gaps between the hafts wood and the eye, you can fill them with scraps of hardwood to decrease the chance of moisture entering into the eye and causing swelling/shrinkage cycles that will lead to a loose head/cracked wood. You shouldn't have to soak the head in oil, it should fit tightly all the way around and top to bottom when completely dry at first. 2 or 3 layers of oil should be enough.
Of course, I don't know that much about this and have only rehandled about 10 axes in my life. YMMV on all aspects of what I've said.
If you do decide to get a new handle you might consider shaving it down if it's too thick. heres a rough guide to a nice thinnish handle for comfortable chopping:
A side benefit of shaving down new handles, or completely making new ones is that you get a lot of nice fire starting shavings:
(purple heart, ash, hickory heart wood and sap wood)