No, not too much of a task. Just didn't want to bore you with a bunch of drivel. After WWI, Hungary is noted as continuing with the same Austro-Hungarian marks. Then on July 10th, 1928 they changed to what is seen on your sporting weapon to become more in line with the 1914 International Proof Conference. Starting at the forward end of the flats with what looks to be a set of antlers with a I in the center is the voluntary touchmark for tubes in the preliminary state or unfinished tubes. This mark coupled with the 15.7mm stamp makes me believe that the tubes were home grown and were proofed separate. For a sourced tubeset from another country one would expect to see a triangle with II in the center which is for an in the white tubeset. If the tubes had been 15.7mm on the final pass it would be 20 bore.
Next is the encircled Saint Stephen's crown over a BP which notes black powder proof. The "FN" below that isn't for Fabrique Nationale but for Füst Nelküli or smokeless proof. I'm not sure on the arrow beside these marks.
Next is the 1st past diameter which is 15.7mm followed by Nem Golyonak, which notes some degree of constriction/choke.
On the underside of the left tube is 1320 which notes the weight of the tubeset in grams. So it should weight 1320 grams. The "2" in it looks suspect and I wonder if the weight was altered at some point or if it was just a poor stamping.
On the underside of the right tube is 408/30 which makes the sporting weapons #408 to pass thru the Budapest proof facility in 1930.
The 16 over C in a rhombus is the chamber info that may have been adopted from some other proof facility. Typically it isn't listed for the Budapest facility but it may just be assumed.
The other touchmarks of the Shield with a N is a later Nitro proof effort. Here's a site with notes on Hungarian marks which appear to be taken directly from Gerhard Wirnsberger's proofmark text possibly with a few additions:
http://www.shotguns.se/html/hungary_1928_-_.html The other marks around the forend hanger are those of the mechanics which either made the tubes, knitted the tubes together to make a tubeset or actually made the sporting weapon. For now I'm not sure which craftsmen used which marks.
Kind Regards,
Raimey
rse