I would think much more than 500mA
Ok then. Next easiest solution, is to use protected 18650 cells, or add protection boards to each of the unprotected cells to make them protected cells.
A protected 18650 is just an 18650 which has a little circuit board hidden on the negative end, upside down so that the bottom of the circuit board becomes a stand-in for the negative end of the cell, the board has a wire (flat strap really) running down to the positive end to power the protection circuit. A protected cell is treated just like any other cell in terms of how you use it, series or parallel.
This page shows you how the protection modules are fitted to an unprotected cell to make them protected cells (this is exactly what you get if you buy a protected cell - well a protected cell that isn't fake and not protected at all, which is not unheard of):
http://www.lygte-info.dk/info/battery%20protection%20UK.htmlIf your cells are unprotected, you can buy the 18mm diameter protection boards for less than a dollar a piece from Aliexpress etc, usually in lots of 10, but of course attaching the wire/tabs may be tricky without a spot welder. Here's
an example which looks like it uses the venerable DW01 and 8205A combination, no affiliation just a random one from my search, you can see that you connect your cell to the B+ and B-, then the back side of the protection circuit is what you use for the negative terminal of your cell. Heatshrink tube around the whole assembly and you wouldn't know the protection board was there.
Note that a protected cell is more like 67-70mm long so some cell holders may not fit, the holders with spring terminals are usually better in this regard (rather than the bent-metal terminal types).