Engagement ring bigger than wedding band

So my engagement ring is a weird size right now, kind of between 5.25 and 5.5. I have thin fingers and large knuckles, so it slides around and spins a lot, but doesn’t go over my knuckle unless I force it. I just picked up my wedding band yesterday and it was sized to a 5.25. It’s a little hard to get on and off but it fits perfectly when it’s on. I thought it would be fine since there’s literally less than .25 size difference between the two, but when I wore them together I noticed the engagement ring sliding on my finger was rubbing against the wedding band and even sliding over it slightly.

I feel like I can’t wear the two together like this because the engagement ring keeps rubbing against the wedding band and I’m worried it’s going to cause damage to both of them. I’m considering sizing the engagement ring down to a 5.25 but the jeweler told me to think about it, because resizing loosens the diamonds. So I’m hesitant resize because of that and because I’m afraid if my fingers swell for whatever reason then they’ll both be too tight.

Will it even make a difference? Will it stop/lessen the problem of the two rubbing against each other if the engagement ring is slightly smaller, to be the size of the wedding band...? Opinions? Anyone had a similar issue?