Robin's method is quite interesting. I might give it a try, but instead of styrene sheets, I might cut a thin part of sprue and use that instead.
Alternatively, liquid putty.....
The problem with sprues is that they do not always have a circular cross section but the pin marks are circles ...
Cutting discs from sprue usually results in curved "chips".
Using sprue for filling large holes is another matter, the large "flags" with company names et.c. on some sprues are really useful to blank of a hole from the inside.
Styrene sheet exists in other forms than those bought for bundles of cash in the hobby shops, many food containers are made of vacuum formed styrene. In Europe all packaging shall have a marking to show which material it is (for materials reuse/recirculation) and the codes for styrene are PS or the number 6 in a triangle.
After a while one learns to recognise the "feel" of styrene, if it glues with your favourite model glue then it will work.