Adding a mini-tank isn't going to fill a tub- it has to be something "real". But mini-tank under the bathroom sink would waste less water (and less hot water) for short draws. With the tank currently located at the far end of the house you cold easily be drawing a gallon or two of hot water for a 1 pint hand washing even, leaving the bulk of the hot water drawn in the plumbing.
Right-sizing the total amount of tank storage volume to the tub size is the best option, and it probably means adding a local 30+ gallon tank, plumbing it in series with the output of the remote tank. Plan-B would be an electric tankless, but even a 20kw version could be painfully slow to fill a soaking-tub, and the expense of upgrading the power to the house & wiring to support it can be daunting. (A dedicated 100A, 240V for the tankless would be needed this isn't just adding a run of romex and big ganged breaker- you may even need to upgrade the power drop from the transformer to your house, depending on your other loads and the existing situation.)