Cheatin - The deck is gonna cheat a bit and you do mention this. But you seem to suggest that this is less of a problem for multi-player games than it is for 2 player games, but I would suggest that the reverse is true. Admittedly that in multi-player games there are more targets for people to play cheating cards on so maybe you will be targetted less, but the problem with multiplayer game is that there are gonna be more cheatin cards about and someone has one to play nearly all the time, meaning you have less chance of slipping a cheatin hand by without being hit.
With the deeds you choose to start with in the deck, and especially the strikes, they should be non-unique as far as possible. I think this is an important point and not one you've specifically mentioned. Since the actual deeds themselves are not so important to you, and the deeds you are using are very common ones that many people use in their decks (especially spell decks), it is a good idea to use non-unique deeds where possible to make sure you can always get them into play and they don't become redundant.
Sure, you have Claim Jumper to fall back on, but if you have the option for these deeds then go for it.
Whilst considering deeds, why 2 Undertakers? I wouldn't consider that this deed is crucial to your game plan and so it seems odd to take up a second space by repeating it. I would have thought if anything that the "Lift Winch" duplicated would be more useful. Also, remember that Strikes are not the only out of town and so isolated deeds - and non-strike deeds are not prone to being claim jumped (and you can still use Lift Winch with them).
4 "Defendin Whats Yours" could be a bit of an overkill in my opinion. You only have a dozen or so deeds in the deck and so I would have thought 3 DWY would have been enough, leaving another space free for another card. Sure, you may well wanna use em after a Claim Jump or so, but I'd still say 4 is OTT - it just means you are gonna cheat more, especially once your deck has spudded out a few deeds and dudes and degenerated a bit. Since you have to boot a dude to use the ability, its unlikely you are gonna wanna play more than one of them a turn anyway.
BTW, DWY doesn't move the dude like you suggested - the dude can boot from anywhere to use the cards ability.
Likewise Claim Jumper. Sure, its a useful card and a mainstay for this deck, but 4 is maybe an overkill, for cheatin reasons if nothing else.
The other jobs are useful - Raids nice cos it allows you to get stuck into an opponents home and Arson and Ambush are always useful for getting rid of unwanted dudes and deeds. Hostile Takeover is a nice alternative to Claim Jumper since it can be used on non-strike deeds, but may not be so useful or appropriate it here and it is only a 10 as well. But Actions are always much of a personal preference to some degree. I might have been tempted to take a Cheatin Card that was useful for shootouts (Sauce for the Gander) maybe but thats all depends on value and what you have available.
I think Buffalo Rifle is worth mentioning - i.e. it is an obvious combo to use with the Lift Winch allowing you to join shootouts at those adjacent deeds without moving there. With that in mind, I think you are underplaying Lift Winch to some extent and it could become a main stay for your deck.
You could think about including Balcony in the deck maybe - allows dudes at the deed to join in shootouts at adjacent locations even if booted - like Buffalo Rifle but better cos it applies to all deeds. Very handy. You can then have Rails and someone else ready to hop about between strikes and call out anyone there and a nice big posse sitting at the Lift Winch just waiting to jump into the fray.
Also useful with Rails, Bartholemew and a Claim Jump - Rails and chum moves to an opponents location and remains unbooted. Next turn you can then play Claim Jump there. Normally this would leave the dude vulnerable since they have to boot at the strike to do it, but use Bartholemew immediately after Claim Jump to slap a Winch Counter down on the newly acquired strike and the Winch Lift Posse are then ready to jump in.
Sidewalk could also be useful on the Winch Lift since you could then move a dude out from there to any deed with a counter to call people out. It is also good to remember that deeds with Lift Winch Counters do not have to be strikes - they can be any out of town deed.
The Home ability is also very cool and not to be underestimated. Things that stop others from moving such as Quarantine or Heavy Rain do not necessarily have to stop you, which is a great way to be able to mosey on out to other peoples deeds to claim jump em whilst they can't get there. Heavy Rain could also be useful to you with Lift Winch, since the deeds will be adjacent - useful to isolate other peoples dudes at out of town locations so you can then pick them off. Its a King as well, and good as a recyclable heart (although vulnerable as an Event), so I'd definitely consider sticking a few in this deck.
Ok, thats about it, not an exhaustive analysis but just a few ideas off the top of my head. Its a good deck mate - fun, aggressive, and with enough tricks and combos to give it a real edge - and one that I'm sure will only get better with more play.