Spurs are for the 'subtleties' of 'advanced' work. They are NOT to make a horse go forward or sideways. I repeat, spurs are NOT for dead-sided horses.
Since your horse is dead-sided, you're going to have to use 'something' to reinforce the leg aid and retrain him. This 'something' should be a dressage whip...yes, dressage whip even if you ride western...because of it's length.
Personally, I would reteach the horse 'forward' on the ground first, but for all those who frown upon such a practice and just want to get on and ride:
Make sure you know prior what the leg aid/s are for what you're asking. Apply the leg aid in a normal fashion...release. If the horse does not respond, you will apply the leg aid again, in a 'firmer' fashion...release.
Note here: It is the RELEASE that tells the horse to move, NOT the application of the aid. It was by the very fashion of constantly pressing and never releasing that got the horse into this situation in the first place.
If the horse does not respond, then you will apply the leg aid a third time, in the 'firmest' fashion and give a good tap of the whip directly behind your leg. I say 'tap', but it might be a 'smack'. That's on you to decide how much reinforcement you need.
And then off you go. Every time the horse starts to suck back behind the leg, you will reapply the correct leg aid and back it up with the needed amount of whip aid, until such time as the horse responds consistently to the leg.
The horse MUST be ridden forward during this retraining. Pulling or hanging on the reins is going to be counter productive. Bumping the horse constantly with an unsteady leg is going to be counter productive. Any sort of inconsistency with the aids is going to be counter productive.
It should take about 5 minutes to fix the horse for that first ride, and then only a few more rides after that to see significant improvement. Within a few weeks you should find yourself only needing to reinforce the leg on the rare occasion and you should also find the horse is more and more responsive to less and less leg aid.