I use the KIV1 tank, it’s HE is very powerful and you can blow away 10+ enemies at a time if you position yourself on some maps like overlooking the Quarry and shoot downward. They can also blow up pretty much any German tanks you find at BR III.
I would say the Panzerfaust 60 is very good for BR III, better then the bazooka.
I would always use AP mines instead of AT mines, even though AP mines are nerfed, I can always get some passive kills because I naturally have evolved my play style to lay them down at key areas. Every time I bring AT mines I will just find myself in a situation where I wish I had at AP mine, but if you evolved your play style to get good at placing AT mines, then go with them instead as tank kills are more rewarding then wounding or killing 1 player.
With the large grenade pouch I would go with 1x molotov, 1x grenade and 1x explosive pack instead of 1x grenade and 2x explosion packs. Molotovs are very useful, you can disable tanks easy as tankers can’t put out fires reliably any longer, and you can also use molotovs to block off doorways temporarily, throw them on destruction-bombs to prevent people from defusing them, throw them into windows to burn snipers or machinegun emplacements, etc. Plus molotovs are natural for soviets.
The radio squad can be useful only if you add 1 sniper cause you can take advantage of the large Moscow maps and snipe of you are good at sniping, while calling in radio strikes. I think a flamethrower squad is offensively better at BR III if you are playing to get on the point, especially in Stalingrad and Berlin, but also they are not as good at long range. Flamethrowers have also been nerfed however so they are not as good as they once were.
A machinegun squad would be an alternative to the flamethrower squad, which would also be better then the radio squad. The fully upgraded DP-27 is good if you go prone and mount it and you can use it as distance if you mount it. As the recent Japan-Soviet event showed us the non upgraded DP-27 with no recoil reduction sucks, so make sure to spend silver to upgrade them and give the machinegunners vertical recoil reduction.
The PPSh-42 Box, the SKS and the SVT-38 are all very good guns for BR III. Consider putting the radio guys in each squad to get full radio strike coverage and give them Winchester rifles as their backups. Instead of 2 AT in the Assault squad, put a radio guy in there. If you want AT, consider a full AT dedicated squad instead of the radio squad, they are very good and can also build AT guns with the engineers, and also put a radio in with the AT squad. You can also put the Mosin with the GGP40 grenade launcher on AT soldiers which can still blow up German tanks and can also kill infantry better then most rifle grenades, blowing up snipers or mounted guns in windows very well.
Soviets have some decent planes too at BR III but you didn’t seem interested in them so I wont bother with them right now.