Would the higher amperage do anything to an older P25? If not would it give it more shots?
Short answer: no; yes.
A battery's charge capacity rating, expressed in Ampere-hours or milliAmpere-hours, conveys no information on how much current, expressed in Amperes (or milliAmperes), the battery will instantaneously deliver. But there is a reason both terms use the Ampere, I'll get to that in a couple of paragraphs.
A battery will not deliver more current than a circuit or device draws from it (this is in contrast to an overvoltage situation: greatly simplified, voltage is force, current is the number of electrons moved by that force). In some failure modes--say, short circuits or other runaway conditions--a circuit or device will suddenly take all the current that the battery can deliver; batteries often have fuses that will open before other damage occurs. Catastrophic meltdown and explosion aren't mere metaphors, here.
Back to mAh ratings... Let's say a given back draws 500mA of current when it's on. A battery rated at 1800mAh will be good (ideally) for 3.6h of operation. 2000mAh will give 4h use. 2800mAh, 5.6h. And so forth.
I'm afraid I can't presently point to alternatives to the 2800mAh batteries from Phase. But now that you mention it, I ought to start looking, as I'll be doing extensive untethered shooting with the P30+ in a couple of months. Naturally, I'll share what I find.