My apologies.
To answer your question first, yes, a ship with engines capable of warp 9 speed can instantly apply a warp 9 strength value to their tractor beam. If you as Captain come upon an adversary and tell your engineer or helmsman to apply a tractor beam and 'don't let go no matter what they try" or similar phrasing, that would imply to go full-value on your tractor beam of 9 in this case. Conversely, the application of a weaker tractor could allow an otherwise unsuspecting target to jam out of there by pouring on their engines.
Given a moderate tractor to start, the opponent would either surrender or ramp their engine 'strength' up, trying to escape. Depending on their size/speed, they would then start rocking your ship trying to escape and either chicken-out and shut down or break tractors damaging both ships. This is equated by the opponent Captain calling for actual warp speed values of warp 1, 2, 3, etc to escape. "Give us a heading of outta-here and warp 5 now, Helm!" "Aye, sir... We're not moving!" "Give us warp 6!" ... They start shaking and damage accrues to both ships until a moment of truth occurs.
So, let's see if I can clear some of this up more.
Paragraph 3, 2nd sentence states the warp value is not necessarily the traveling speed. Warp factor in this regard is a way to loosely equate tractor strength to engine strength yielding towing values.
Similarly, this allows for two captains to slug it out such as Kirk and Dr. Severin. By these rules, Aurora lost for its size/speed vs. 1701's size/speed and paid for with blown engines. Aurora was traveling at whatever speed, encountered 1701 and her tractor beam. Whether Severein told his crew to increase speed, add more throttle or whatever, the engines were pushed and pushed harder. The easy way to say that in game mechanics is warp value.
The tractor factor could be named anything as its simply a number from 1-10 or so. Equating it to warp speed is a convenient reference-frame that ties it to a specific ship class without the need for construction charts. This also gives relative strength values of beam, light to strong just like phasers, for example.
We see with Cpt' Christopher's F4 that even the lightest strength tractor will soon destroy old-style craft. While with Aurora, we see that a ship has to push their engines past safety limits to fight a tractor beam and if they cannot escape, they blow up or shut down. Same for the tractoring ship which will shake and buckle as a tractor is fought, given relative sizes, etc. If the Tractoree does break the tractor, there should be structural damage to both ships, worse for the loser in all cases.
Kirk never said what strength tractor to apply, just to apply them. It was either then Scott's or Sulu's job to apply the correct strength of tractor to maintain their need.
1st edition simple combat system says once a ship enters warp, they are off the battle board. And indeed, if a no-gooder comes across a Fed patrol vessel, they are going to try and warp away. By equating tractor Strength to warp value, the patrol vessel's Tractor Strength negates or hinders the bad guys escape. The patrol vessel could be at a stand-still with the warp 7 factor power value going to the tractor beam. They could be traveling warp 7 with the criminal ship as well, as long as they are at relative speeds.
Equating tractor value to warp value also derives from and demonstrates that smaller engines with slower speeds on a lesser vessel weight create weaker tractors than bigger engines with higher speeds on heavier vessels. Similarly, two big ships each with different engines speeds (i.e. power plants) will produce different tractor strengths. Without any charts, the tractor strength of a million-ton ore carrier of warp 2/4 value will create a tractor strength of 2-4 million tons. Any ship size, any speed value and you have instant, self-derived stats.
Let's round Connie to 200,000 tons for simple math, at a warp 6/8 will produce at most a tractor-value of 8x200,000 = 1.2 to 1.6 million tons. If bad guy of the week got hold of that ore carrier to capture Connie, ore carrier would fight to control Connie at warp 2 tractor value but at warp 4 tractor value would own Connie outright. Similarly there is no speed (engine output) Connie can make that could beat that particular ore carrier's power plant when maxed out.
This system keeps tractor beams independent of the construction charts and the need of equating particular model tractors to particular model engine types and so on. This keeps tractor beams generic in nature, tied only to overall speed and tonnage. This allows a 100,000 ship of 5/7 to tow 500,000 of weight at a given distance and new top speed without the need to cross-reference charts or tables. Simple equations done on the fly and applicable to all, equally. (One could say that a given Species (Klingon, tellarite, whoever) or corporation/planet produces better or worse tractor beams. That would be GM discretion based upon the generic formula presented.
My primary concern is how to apply damage.
Ship's rocking each other should buckle frames and burn components. How much and how fast?
We have only the Aurora and Cpt. Christopher's F-4 to show us tractor beams can crush and destroy. This should be based on engine strength as a lesser ship of lesser engines would not be as strong. Warp value again, is a handy and very easy 1-10 factor and applied to ship tonnage creates a believable towing strength of however many tens-to-hundreds-of-thousands of tons depending.
A ship can tow its own weight at any speed at 'no cost'. Heavier weights at higher speeds create additional stresses. Fights guarantee harm.
I need a formula to derive stress damage that also plugs all this into the STCTS with as little clunkiness as possible. Eliminating construction tables, brand model numbers and that stuff helps keep it smooth.
At least I hope so.
And thank you for reading all this to you who have! I deeply appreciate any help and critiques to make this better. I will also credit you when I go to formalize all this into widespread release.