Electronic – Bulk capacitors/charge reservoir for large pulse current/current exceeding supply

The calculation is straightforward. The capacitor size is simply a question of how much voltage drop you can tolerate over the duration of the pulse. The average current from the battery is a function of the duty cycle.

ΔV = I × Δt / C

Solving for C gives:

C = I × Δt / ΔV

Let's assume you can allow ΔV = 0.1V. For your first example, this works out to:

C = 25 mA × 25 ms / 0.1 V = 6.25 mF

The average current draw is 25 mA * 25 ms / 2.5 s = 0.25 mA.

For the second example, the numbers work out to:

C = 50 mA × 100 ms / 0.1 V = 50 mF

Average current = 50 mA * 100 ms / 1.0 s = 5 mA.

Dielectric absorption (DA) is much (5-10x) higher for polyester capacitors as compared to polypropylene, so losses will be higher, which could cause problems.

There may be other differences in construction that would affect pulse applications, however they are not inherent to the choice of dielectric.

Edit: I don't think the capacitors you show are necessarily suitable- the pulse current could be very high, which those parts are not designed for (my second original paragraph above). Consequence could be slow or rapid destruction of the capacitors as the metallization blows off the mylar and perhaps shorting of the plates.

There are other types of capacitor easily available which could be substituted but I think I'll let others suggest them. This seems like a pretty dangerous project.