I've been rewatching the series and I noticed something I'd missed before in
CAN'T REMEMBER THE TAG SO SPOILERS
"the doctors wife". When he was moving from the (sort of like a bubble universe on the edge of our universe but not really) to our universe he said it was necessary to delete 30% of the rooms. If we take that amount as semi-reliable (as opposed to more than necessary) it would mean 60% of the existing rooms were deleted for fuel 30% there and 30% back. This is just to move out of the universe to one that's a (see above ) while obviously going right out and back into another would take more. Now that kind of power supply is obviously more than the type 40 model can handle but a type 70 or a type 89 or a form 10X? I think they could do it especially the form 10X ones which had multiple copies of the eye of Harmony and power sources that can take them anywhere in the timelords understanding which would include places they couldn't draw on the eye of harmony (too far forward, back or sideways). So I'm thinking it is possible for a TARDIS to still jump universes just not the doctors one (especially given the cybermen invasion at canary warf).
It's less about the maths and more about the process. That is the TARDIS getting more power by deleting rooms was able to get outside the universe. Therefore more power still could get it into another and the later models were more powerful.
Actually I'd imagine its quite possible, laying aside the example you give there are plenty of others. Classic Dr Who had them winding up in E-Space and needing to find a way back complicated by the lack of proper co-ordinates for that univesre, in the one where they get stranded in the world Rose winds up in he comments they used to pop back and forth casually but the walls have thickened now. then there was the 3rd Doctor's trying to bypass the timelord's confining him to earth accidentally moving him sideways to that inferno universe and there are others.
However I think the TARDIS doing the travel especially if your placing it in current who era would need to be specially designed for the purposes rahter than simply being a more advanced model. The issue isn't technology as we've seen an obsolete Type 40 is quite capable of making the trip but its power that's the issue. Newer models have better technology but the power is still the same drawing from the Eye of Harmony and from my understanding even the most advanced war TARDIS still did that they just had multiple copies allowing for more power to be drawn from it at any one time. To use modern technology The Doctor's TARDIS is hooked up to run on 120V power, a Type 90era is running on 240V and the WAR TARDIS runs on 415 however they all draw their power from the same power plant rather than producing their own and if you cut the power lines by moving them to another dimension they have nothing more than what they can cobble together from generators and capacitors (deleting rooms and the time lord giving up some of their own energy). In this case the more advanced models could actually be in a worse position as they need more power for full functioning.
So if your going dimension hopping or moving outside the range of the Eye of Harmony link you need a TARDIS that's been built or at least modified to allow that to happen. The Doctor's has been jerry rigged to drain stars or rifts for power supplies in addition to the deleting rooms for emergency thrust or him giving up some power. Indeed it seems in the current series (as in S1-S11 new who) he's slowly been modifying the TARDIS to eventually use its own mini-eye. Which is the better option an experimental TARDIS that has its own eye of harmony as a power source in addition to the main link so it can jump dimensions and still continue operating at full power.
My head canon is that this is a deliberate design decision by the Time lords as by tying all TARDIS to the eye of harmony they not only limit the extent by which a rogue Time Lord can travel (no dimensional transit, no moving outside the range of the eye of harmony) but potentially have a way to cut off power and strand a rogue Time Lord if needed like that did to the Doctor. This being why he had to work on the console outside the TARDIS it was because he was actually tapping the London power grid for his experiments as the main link to the Eye had been cut. Which is also why he modified the TARDIS design to allow transit in the future when that happened again. So what you'd need is either an experimental model before that practice became common (In the game it'd be an obsolete or antique model) or one that was specially designed by either a rogue faction or the CIA for their use until you get to the time war era designs (advanced, GM approval) where some might have been developed for special situations. Which ever justification you use it'd need to be part of a limited number if your looking for one that can do the reality hopping on a regular basis, for one off adventures there are ways you can cobble together a solution and the lack of power can provide a nice plot hook in tself.
Also I'm aware I'm replying to my own thread but my thinking has changed since it was started.