I'm a big believer that forcing a senior leader transition in a pack or troop is fraught with problems. It leads to hurt feelings and politics - never a good thing. I'm also a big believer that you have to look for the good in volunteers - even a COR.
I'd try to handle this by developing an open working relationship between the key 3. Do you all meet regularly as a group? In that forum do you all speak honestly with each other? I'd use that forum to work out differences of approach. There, be brutally honest with each other. But, outside that forum - have each other's back.
On the specific issues you mentioned:
- stickler for rules - embrace this. Yeah, no one likes rules, but they become accustomed to them.
- taking over at Pack meetings - in that key 3 meeting, I'd be honest with him. "Hey Joe - showing those presentations at Pack meetings is really boring. We shouldn't do that. Also - you jumping in undermines my leadership as Cubmaster. If you want the floor, let's arrange it ahead of time."
- fighting with parents at the PWD - "Hey Joe - Tom is our PWD chair. It's his call on rules. It confuses things that you jump in on decisions. We really need to empower him to be in charge. You shouldn't engage with parents on that. Instead, please refer questions to Tom."
As Cubmaster, I had some real difficult conversations with our COR. Because we were honest and direct with each other n private, yet supported each other in public - we left the roles great friends.
Sorry - my post was confusing in hindsight. I am suggesting that the SM enlist adult volunteer support for uniforming - not necessarily that all the adults uniform.
As Scoutmaster you want adult support for transformative decisions. Yes, we'd like to think the adult volunteers will support the Scoutmaster, but it's still important for the SM to get folks behind a big decision. Going to a leaders/committee meeting and having a frank conversation about supporting this decision is helpful. That helps ensure that word gets around. It also helps that leaders encourage their own kids to uniform as well.
Since you brought it up, I'm in favor of adults feeling empowered to uniform. Scouts notice ASMs and see what they do. So, if the Scoutmaster is saying "uniforms are important", but the ASMs are out of uniform or poorly uniformed, that's noticed.
On the other hand, if the adult treasurer, advancement coordinator, committee chair, etc. are uniformed that sets even more examples. If I were SM, I would ask the ASMs to uniform if possible. I would encourage the committee members to uniform if so inclined. We have many adults who show up to meetings in uniform (and most do not have beads). There are other subtle benefits.
Adults seeing other adults in uniforming encourages volunteering.
It helps committee members feel a closer connection to the troop.
It makes it clear to visiting families who they can approach for questions
In an era of needing more registered adult supervision, it helps everyone know who the registered adults are.
It's not uncommon to have 10+ adults in uniform our typical troop meetings - more at a COH.
BTW - yes, we get good participation from Scouts wearing uniforms. We've never needed to do a uniform inspection to encourage that. We rarely even have to say something to a scout.
Here is where I disagree with @ParkMan, the SM was the only adult who wore a uniform in our troop. The rest showed up in their best work clothes. The ASM who was a coal miner looked pretty rough, but one of the most caring men I had met in scouting. I never saw a committee member in a uniform until my sons joined scouts. Still think it's dumb. Why does an MC need a field uniform? To set off his/her beads?
None of those adults bothering with uniforms, and guess what? I made a point to look sharp every meeting and hang my pants creased in the evening. Shoes polished every Sunday. Inspected patrols every couple of months just like the SPL's before me had done.
You're the only adult who the scout needs for an example of a sharp uniform. You don't need your adults to uniform. It's not their program. You need them to admire your scouts. You need them to be kind to one another. You need them to turn into wallpaper as the scouts run meetings and activities.