A few things come to mind...
1 - Wiring across the batteries will help with the compressor tendency to stall, which is hard on just about everything in the mix because they need to draw more than normal current to get back up to speed.
2 - Replacing the caps with a higher voltage "equivalent" will help the caps handle transients they experience during normal switching that occurs while driving the compressor motor(s) - To a point. Generally speaking a higher voltage cap of identical capacitance will have a higher ESR, which means they will generate more heat internally... In the case of electrolytics, this will try to drive the moisture out of them sooner, making them age quicker, bringing it somewhat full circle. Generally, I go for the next voltage up as a balance. IOW, if the original calls for 16V, replace with 25. If original is 25, replace with 35... original 35, go with 50, and so on.
3 - Applying so-called "bypass" caps across each electrolytic will help them handle normal switching transients more efficiently. This is usually best done by soldering them *directly* across each electrolytic, with the leads as short as possible, on the foil side of the board in a one-for-one relationship. By forcing the highest frequency switching currents around the 'lytics, these spikes won't be dissipating as much energy inside the caps (hence the name "bypass"). Small tantalum caps on the order of a couple uF each are usually sufficient for this purpose, and at the lower voltages we're talking about here, really are ideally suited for the job.
4 - Keep things cool by adding a fan if necessary. Even if the air circulating over the board isn't as cool as it should ideally be, any circulation is better than plain convection (which by definition requires heat to work) and will help.
5 - Increase the overall capacitance. This can be tricky because of space requirements, but if possible, up the total capacitance by increasing the cap count. It's better to use more of a smaller value than a single large cap to do this, as part of the goal here is to reduce the overall reservoir impedance, not just store more energy. A reservoir that can't deliver the necessary current when the transistors call on it to give the next push, isn't able to do it's job efficiently, and as mentioned above, will generate heat, and prematurely age the caps. Also, it will do you little good to pile up a bunch of caps on a couple of leads running to the original reservoir cap traces on the board. Inductance and resistance will largely negate your intent, so this one may be only minimally practical, if at all, in many cases. It depends on the board layout and how closely you can slip them together at the location of the original caps.
Ideally you'd do some combination of all of the above, but this isn't always practical, so you just have to go with what you can.
Hope this helps...