OP: have you weighed your new bridge prior to mounting it? With all dimensions (like feet width, depth & position, height of bridge & location of strings) hardly changed, I suspect there is a difference in weight between the 2 bridges which causes a change in one of the instrument's resonance frequencies. Bridge balance & orientation can also contribute.
Do any of you have non adjustable bridges and swap them out?
Yes, one one of my instruments, a fully carved one, I have 2 bridges with a slightly different height, 1 French & 1 Belgian. Sound-wise I find it difficult to hear a difference between them, but the Belgian being slightly longer-legged & lighter seems a bit more powerful & brighter. Also, visually I prefer the Belgian looks. The Belgian is slightly lower in string height. Lately I don't change the bridges, when string height needs to come up I slide a 0.75mm wooden shim below each feet, and take those out as required. "a 0.75mm wooden shim" = a bit of veneer.
This very old type of height adjustment is essentially a comparable approach to Don's bridge above, though each full turn of his foot might be more than 0.75mm (I estimate that at about 1.1mm). And the other difference is that the steel adds a little bit more weight, and more flexibility. In a properly balanced bridge flexibility in the up-down direction is irrelevant (in the absence of load in that direction), but on a strongly curved top flexibility in the sideways direction is less desirable. In both cases you need to take the tension off for height adjustment; neither of them are suitable on a set.
I know there is an internet document somewhere of some student comparing the effects of various height adjusters, I remember having scanned it, but the results have not stuck in my mind, for one reason or another. The effect of the extra weight on the location of the adjuster is easily assessed if you make 2 small jigs (with a weight equal to the weight gain due to adjusters). Put them on to simulate with adjusters, take them off to simulate without (no, to be without).
In some cases such a localised weight difference can impact resonance modes, but I have not actually observed that. What I have seen are minor effects along the lines of the old adagio: less weight = louder. Also that low, the extra weight acts as a little bit as a mute, though obviously not nearly as strongly as high-up on the crest, where mutes are normally placed.