The fact that the engine moves sideways as you explain indicates that the splines are as bad as they can get already. The only way the problem could get worse is if the motor mounts become affected. In my 30+ years experience in the trade,I've never heard or personally encountered a 1977+ V4, V6, or V8 tearing up motor mounts but I suppose it could happen.
However, should a mount or two break, the engine isn't going to move very far as the metal retaining portion is still there. Putting the repair off until later will need to be your judgement call though.
What it would cost to have a shop do the repairs depends on the honesty of the shop, the mechanic, etc, and of course their hourly rate.
Parts are rather pricey.... my price books only go to 2010 due to being retired and at that time the steering arm alone was around $700. Normally, time-wise... it would take me about 3 or 4 hours to do the job. The flat rate manual says 2 hours but there's always that stubborn bolt, the one with the rounded off head, then the run out, adjustments, whatever.
Look the engine over closely, it's not that complicated... just make notes, and take pictures before you disconnect anything.