Should I pay to balance already "balanced" tires?

Long story short I swapped my winter tires to another set of rims over the summer and assumed the shop balanced them. I went to put them on and they feel unbalanced. I moved a couple tires around and the vibration changed so it might be only 1 or 2 tires that are unbalanced.

I went back to the shop and they said since it done was a while ago they can't do anything and would have to charge me again to balance them.

I'd rather give my buisness to another shop but also am curious if I need to have all 4 balanced or if maybe they can check and only charge me for the ones that are unbalanced. Is that possible or would they just charge me to do them all?

Also any advice on if it's possible to get the original shop to do it for free? It was about 5-6 months since they were mounted and they've just been in my basement. Both the rims and the tires had no balance issues before. Rims are OEM and tires have less than 15k on them.