Smolen to show GF with 4M and 5 in the other major. Start with 2C Stayman and follow up with a jump in your shorter major if a fit is not found. You can show 4M and 5 other major while making the stronger hand declare.
Are you allowed to use the Kaplan Inversion? Where 1H-1S acts like a forcing 1N and opener rebids 1N with 4S. You still can use 1H-1N* to show 5Ss. That would allow you 2D* as 18-19 and 2H as a weak Two bid.
I played a lot of Roman Club at the Congressional Secretaries Bridge club in the late 70s or early 80s. I also played Roman Club as a change of pace(once in a while} over the last 50 years.
This was much like the style of some Italian players in the 60s. Blue Team Club players overcalled @3-12HCP and doubled with 13+. Responder was not supposed to expect more than 2 cards support in any given suit after a double.
Gazzilli on Bridge Winners has a number of concepts. One is 1S-1N*-2C*(clubs or strong) -2D*-2H* denies four clubs and also not strong NT values. I like to use 1M-2C* to show a 2/1 type GF or a limit raise. 2M making 2 at your table and 3M-1 at the other table is a fairly steady source of MPs or IMPs.
Did you notice that 4N showed 20+HCP and 7NT promised 25+? This means that you overbid by 4+HCP for 4N and by 9+HCP for 7N. Bidding slams on HCP is often suggested as 33 for 6N and 37 for 7N. Your results would likely greatly improve if you allowed partner to 'limit' their values.
OMF(Other Minor Forcing) is a common method after a 1NT rebid. 1D-1S-1N-2C*-2H showing 4Hs and denying 3 spades. Now a spade rebid is forcing and you can bid to slam. You really do not want to bid 7S with nine trumps missing the Queen.