Hey there, first of all, I don't think you're alone in this gripe with the use of temporal tokens in TSS, the level you are on in particular has a mix of good rooms and pretty poor rooms which just require guess work. They aren't really explored properly until much later in the game in my opinion. There are a bunch of usermade holds which use them better.
Secondly, a couple of general points about Temporal Projections. For one, if Beethro and a TP are the same distance from a monster (this is worked out via Chebyshev Metric), the monster will target the temporal projection which came earliest in the time line. This means that if current Beethro is one square away from a roach, and so is temporal projection Beethro, the roach will target the temporal projection, if there are multiple projections, the monster will target again, the one that came first (that is, the one that, if you right click on it, has the
highest number). Hopefully, this will help.
Also, try and give yourself plenty of time to do everything so that you don't have to worry about efficiency, to be honest, there's not a lot you can do with these future Beethro prediction rooms other than to consider where your danger points are and to stick to areas where monsters can only come at you from a limited number of directions.
Serpents can be hard to predict anyway if you're not super familiar with them, and so an added inclusion of a temporal projection obviously doesn't help. IIRC, there aren't a whole lot of serpent rooms in TSS because they can be pretty hard to manipulate. If you're still having problems with them, then there are some guides around here somewhere. There is a brief description of how they move
here.
As for the room in question
here is the hints board for it, and if you're stuck after reading that, then just post again over there, and I'm sure one of us will be happy to help you out.
Finally, I doubt there are any tools that could help. There aren't any custom clocks which can help, and a mod which allows you to move Beethro and TP in parallel also doesn't exist and probably won't ever as it partially defeats the 'puzzle' in some of these rooms.
Hope this helps!
EDIT: Post clash! The advice above outlines a lot of the same stuff as I do!
____________________________
Member of the Snake Appreciation Society
One of your local HAs.
My stuff:
Click here to view the secret text
[Last edited by navithmastero at 06-09-2018 02:40 PM]