One of the reasons I purchased the Fender 2 collection for Amplitube in my recent plug-in spree was the 67 Blackface Fender Super Reverb. I wanted it for the tremolo and the underwater "surf" reverb.
Haven't messed with it much but I saw this thread and set out on a search.
This one is free: http://adammonroemusic.com/free-tremolo-vst/tremolo-vst-free.html
It is pretty "normal" as tremolo goes, there is also a panner. I tried it, seems to sound fine for what it is. Smoothing option?
This one looks interesting and I'll have to give it a spin also. https://bedroomproducersblog.com/2018/01/11/hy-plugins-tp2/
There is a nice variety of waveforms for different effects, a bit more sophisticated + a smoothing option.
As always, if something is "free" on the internet you are the product, not the customer. This is why God created fake gmail accounts!!!!!
Here's a thought, since tremolo is amplitude modulation maybe you could run two instances of the same track with the same tremolo settings and then gate one of the tracks until all it does is make that glitch sound you mention. Then, reverse phase and cancel it. I haven't tried it, your recent posting of your link on using phase reversal to make things go away has been rolling around in my brain for a bit.