I think it's also worth noting that the bridge of the Enterprise-A
at the beginning of TFF looks nothing like it did at the end of TVH. We never saw more than the bridge in TVH, so the rest of the ship could have looked as it did in TFF from the time it was built. But the bridge was clearly shown. It was either remodeled at some point, or a new bridge module installed. So it's not like there was 24 hours between TVH and TFF. There needed to be at least a little time.
I tend to favor the idea that they went on a brief shakedown cruise for a week or two, encountered problems, and came back to Earth for repairs, which were underway when we join them in TFF.