Not surprising... with the larger tyres you have a significantly increased your "top gear" final drive i.e. lower revs for same speed ... which may be a bonus unloaded for fuel consumption, but you then have a lot less torque because you're down possibly around 300 rpm between 90-100 kph which is why the auto is finding it difficult to maintain lockup trying to pull an additional 1 tonne plus of caravan.
I suggest that for towing you get a set of wheels with smaller diameter tyres... it's a lot cheaper than trying to replace the F/R diffs with lower (numerically higher) final drives...
MY99 RR P38 HSE 4.6 (Thor) gone (to Tasmania)
2020 Subaru Impreza S ('SWMBO's Express' )
2023 Ineos Grenadier Trialmaster (diesel)
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