LMGs on grens shred PPSH cons. I don't see the issue here. The PPSH upgrade forces the Cons to close in, which is the also the range where LMGs shine.
This is a good point. If you are fighting a horde of cons with PPSH you need to set up a line and draw him into it. Keep grens well up front with lmg's and a 42 well back. This will force the cons into a lose/lose battle. If they stand the lmg grens eat them up. If they charge to deal damage the 42 suppresses them, reducing their damage, and ability to close the battle. If he has 3 cons you should also have 3 units.
To bolster this add in a HT to reinforce in the field (not to attack!) and you will be able to turn the tables. Nice thing about con blob is once it retreats you can have freedom to cap since he will have few units on the field. Move up the 42 and then place an s-mine field on the flank and use it to force them back once they charge in again.
It is still annoying that cons can throw molotovs from suppression, but once your 42 has suppressed them immediately pick it up and move it back slightly. That gives you more time to pin them. You can also keep a reinforce point nearby. MG's can usually reinforce faster than a molotov can burn (depending on crits of course).