Hello Ian,
I think you may have misunderstood the comments about your 85Ah battery. It is most likely that if the battery terminal voltage fell to 10.5V under load, then either the battery was not fully charged, or it was old or damaged.
The ability for a battery to hold a full charge diminishes with age and usage, and that would affect the amount of current it can provide.
Even though caravan movers may be rated to consume 60A, that is the peak current, and is only likely to be needed just as the mover spins up to speed. Once at speed, the motors will only draw 15 to 25A unless you encounter an obstacle that you need to climb over. A healthy leisure battery should be capable of providing a continuous current of 25A without distress, with peaks well in excess of that.
In general, the main difference between 85 and 110 Ah batteries is the total capacity, not the peak current discharge rate. It really affects how long the current can be supplied. As most movers are only used for a few minutes, the total power used is only a few Ah, and are unlikely to flatten a good battery under normal usage.
If you have been to any of the caravan shows where movers have been demonstrated, If you were to ask the companies how long their display batteries last before recharging will probably elicit a reply of about 4 to 6 hours of extensive display hours, and that is much longer than you are likely to need when on holiday.
Just a quick calculation, if we assume you need to use your mover for 5min, to position your caravan, then the 25A for 5/60 of an hour gives a total energy usage of only 2.5Ah so to allow for variations in surface you will most likely use less that 4Ah in total - not a great deal compared to the total capacity of either an 85 or 110Ah battery!