There will not be any damage when a person installs a larger capacity battery than called for, but charging will take longer. In an extreme case the battery will never achieve a full charge. For the opposite condition where the battery is undersized, the battery could be damaged by over charging (too fast or too long) and will swell and have bulging of its case. Today’s smart chargers (micro processor controlled) help to minimize this risk.
In general, the battery charger will provide 2.45 VDC per cell to be charged. The resulting current flow is dependant on the charger source resistance, the battery internal resistance and the battery’s voltage at that time. The nominal cell voltage is 2.2 volts. For sealed lead acid batteries, this current flow must not exceed 15% of the battery’s Amp-hour rating. Flooded cell types can go somewhat more than this without damage. No doubt you’ve seen chargers rated as 2A, 10A, 75A etc. This is related to the internal resistance, and hence the maximum current it could deliver into a large fully discharged battery (1.8 volts per cell). Some chargers allow you to select a charge rate by switching in a bit of extra resistance to slow it down. Often they label the switch as a battery type selector. For TT converters, they size the charging circuits in-line with the above parameters.
For the OP’s desire for a group 29 battery, I still think the biggest limitation is going to be physical size. The ability to achieve a full charge is a grey area. It has about 40% more Amp-hours than a group 24. Not a huge amount really. To know the fine details of his particular set-up, contacting the maker of the converter would be worth while.