The Ash1 will also work for gutting, skinning. The skinny ash (.22) might be your choice. I just used a CG Ash1 (.30 thick I think) to bone out and butcher a quarter elk the other day. Worked fine.
You might be able to pick up a new one from the company store for close to what you are looking to spend. I think they are $302. But that is before shipping and tax. Look through the exchange and you might find one for less than that with a sheath.
I also think a BATAC will work great for that also.
You might want to also consider a SAR5. They go for a bit less. Busse, Infi, great blade shape for skinning and gutting etc. The lack of a choil makes for more usable blade length in a smaller package. Some aren't fond of the handle shape, some love it. Just personal preference. There are some on the exchange right now for much less than your "max" Some are less even with a quality sheath. I think I just saw one for $240 with a great sheath. Did I mention they were infi? (and no, they aren't mine for sale)
The GW will be shorter than you are looking for. I used it also quite a bit in butchering that elk. The blade shape worked great. I think it would make a good skinner, but at 3' it is a bit short to be your all around knife. If you were carrying a longer and shorter blade no problem. When I was slicing large pieces of meat into steaks and roasts, the blade was a bit short for that work. Not that it did not get it done, but a longer blade like on the ash, and even on my SS made for a cleaner easier slice.
The BAD would keep an edge longer, as it is at a higher hardness. But, It might be a bit thin if you are going to be splitting rib cages and such. I think it would hold up, and if you broke it or ruined it while doing normal stuff like that, the for life warranty would take care of you. I have seen pics of people batoning the BAD, and one crazy guy who batoned it with the spine of another Busse knife. But again, the BAD blade is only 3.5 inches long.
I also think you might want to take a look at Scrapyard's on the Busse exchange here. They have a lower price point, and are also awesome. They have the same great warranty, made by "family". They have a very avid following. You might be able to pick up one in the size range and satin finish, with a nice sheath for less than your max limit. You could probably come close to getting two different models for about the same you will spend on the Infi. However the uncoated scrap yard knives will be more rust prone than Infi. They are SR77, a modified jack hammer steel. They are super tough (as proved by Noss on knifetests.com)
Infi is pretty darned low maintenance. I have put them away wet, and dirty. I have not had any rust yet. You can get some greying or patina with the right stuff on them (I have not had any yet). I have seen some pics with light speckling of spots. (as long as it is not some of the recent Sarsquatches/Jack hammers/hell razors competition edges, with the decarb left on, those are pretty rust aggressive until you remove the decarb).