Side plate differences on 113
I'll post a few that I've come across on different web sites.
113 Black, external drag access opening -late 1930s to late 1970s
113 Black, sealed drag housing -early 1980s to present
113H Black, external drag access opening -late 1960s to late 1970s
113H Red, external drag access opening -late 1960s to late 1970s
113H Red, sealed drag housing -early1980s to present
By the way, you mentioned that the plate was marked "113H". A quick way to confirm if the reel is truly a high speed model is to check if there is a right side bearing (cup set into the plate) or bushing (w/ screwed in hex head).
There are three variations in 12/0 senator spools, one is not desirable.
The very early senators had a chrome plated bronze spool that was made in three parts. With stretchy lines like mono, these spools are bad about spreading which will destroy the reel. There are no replacement spools for these reels and modern spools won't fit. These early senators also had bushings instead of ball bearings.
The three piece spool 12/0s were replaced with a ball bearing reel that had a one piece chromed bronze spool. They are IMNSHO the best of the 12/0s.
Some time in the 90s, Penn replaced the chromed bronze spool with a aluminum spool. These spools are as strong as, or maybe stronger than, the chromed bronze spools but the aluminum spools won't hold as much line.
All the parts will interchange between the aluminum spool reels and the one piece chromed bronze spool reels.
A 30 or 40 year old 12/0 in good shape, will handle anything a new in the box one will, as long as you put new HT100 drag washers in it. Handle color and things like that are for collectors to worry about.
If you can't see the spool arbor ,,,to see if it is a smooth 1 piece or shouldered 3 piece. Look at (if possible) left side plate. Center of side plate holds either smooth surface ball bearing or stand out bushing knob.
Get bearings
Penn 6/0 spools
I think the Special Senators are the H model and always used chrome over bronze spools. If I'm right on that name, The Senator ll was the HL model and used a aluminum spool. I may have that backward. If not, the HLW series would have all been Senators ll reels. Both the H and the HL, had the same high speed retrieve. The HLW is just a wide frame version of the HL. All Three version have red sideplates, except for the very early ones which have maroon sideplates.
The first 6/0HLW used a frame very similar, if not identical to the 9/0. Over the years, Penn has upgraded the frame at least twice, without changing the model designation. The latest version has the one piece aluminum frame.
There may be another version of the 6/0W. I saw a reel in a Houston pawn shop a couple years ago that was definitely a Penn 6/0wide. It had what appeared to be a wide chrome over bronze spool. At the time, I didn't realize what I was looking at and didn't even give it a second look. I went back a couple days later to get it, and the reel was gone.
I'm not sure if that spool was made by Penn or some machinist somewhere(not too hard of a job, if you have the right tooling).
IF it was a chrome over bronze spool 6/0W and all the parts were Penn, that is one very rare real.
Penn ought sizes
Here is the way the Penn Senator model numbers broke down. 110=1/0, 111=2/0, 112=3/0, 113=4/0, 114=6/0, 115=9/0, 116A=10/0, 116=12/0, 117=14/0, 118=16/0.
None of the other current manufactures use this old system and Penn only uses it on the Senators.