Super-Simple, one-app, multi-track video (that's handled like Audio in a DAW)?

[MODS: I didn't see this addressed anywhere else -- please feel free to move to/suggest somewhere more suitable for this post or to direct me anywhere you think might be helpful. Thanks!]

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Hi, everyone.  I'm still fairly new to Reddit and learning my way around. 

TL;DR: I'm an orchestra teacher looking for a simple, all-in-one (and, ideally, affordable) app for PC that will let me record and monitor multitrack video/audio to make simple, time-aligned, "Brady Bunch" style music videos without having to go through intermediate steps or apps.

Most of this is projects for the kids at school (I'll record all the parts for a piece we're working on and post the composite video and the individual tracks for them to reference and play along with), though every now and then I'd like to do a fun little something for myself.

I've used easyvirtualchoir.com for this but, while it's an amazing resource and I'm thankful for it (it was a real boon when we were stuck teaching online, years ago - many thanks to the person who made it), it hasn't always been reliable for me (latency varies with the quality of your internet connection and I've lost work a few times when it's refused to add tracks or frozen up in the middle of a project) and I want to be able to do the work on my computer without an internet connection.

I recently did a couple of small projects with Openshot (free video editor, but doesn't record) and the built-in Windows Camera app.  That wasn't too bad -- I like the UI (so far) in Openshot and I could time align the videos by hand by counting/clapping at the start of each, but this is all takes a lot of time and resources to get right (particularly if you don't nail each take the first time -- lots of similar-looking video files to go through -- Openshot also crashed several times, but I'm not convinced that's all the program's fault -- it happened the first time after I installed Movavi, though Movai wasn't open at the time, but I digress...)

I also added Audacity to the above mix (Openshot + Audacity + Windows Camera app), which has some advantages (you can handle the audio more neatly -- as well as pan tracks, etc., if you want to), but still involves a lot of intermediate steps and extra video files to sort through and time-align by hand.

A few days ago, I downloaded Movavi, after reading and watching reviews of it (including at least one featuring the kind of videos I want to make) and seeing that it could record camera video  (I got their Video Editor Plus, lifetime license, for $100).  When you record audio-only, it does it within the editor -- I think that you can handle it and monitor multiple audio tracks while recording just as you would in a DAW like Audacity or Garageband -- but when you record camera video, it launches a separate app and there is no way (that I can see so far), within the app, of listening to the tracks you've already recorded while laying down a new track (which was my whole reason for downloading it and paying the hundred bucks in the first place).

Using multiple apps and aligning tracks by hand might not seem like a big deal, but I'm stretched thin and short on time as it is... stuff like this happens on my own time, at home, or crammed-in over a lunch break. I don't need fancy transitions or effects and, 99% of the time, I'm more than happy with the mono audio from a simple USB mic (I keep a Samson Go Mic in my backpack).  I want to be able to throw down the tracks (while HEARING the other tracks -- this is key -- as I would if recording multitrack audio in a DAW like Audacity), trim the beginning and end, and export...

99% of the time, It'll be just me recording all the parts, so if the program only allows one video to be recorded at a time, that's fine -- I just need to be able to hear the other parts while I'm recording and, ideally, have everything time-aligned already (as it is in a DAW -- at least once you've set the latency correction before recording).  

Basically, I'd like to be able to with video what I do (just the basic functions) with audio in a DAW -- or to do what I already do in Easy Virtual Choir, but more reliably and on my computer.  The simpler the workflow, the better. 

On the rare occasion when I want to do something more polished, I'll be okay with taking extra steps, but the majority of these supposed-to-be-quick little projects won't happen that way.

Apologies for the egregious length of this post -- this isn't an absolute need (I'm able to make these videos now, just not as easily or reliably as I'd like) -- and maybe such an app doesn't exist -- but I'd appreciate any help y'all can give!

Thanks in advance!