Upgrading axolotl tank setup - advice please!

Hi everyone! We're in the process of upgrading our axolotl Max's tank setup. He's currently in a 67l tank (which is typically filled to about the 55-60l mark), but we've been having endless problems maintaining a stable cycle, with frequent ammonia spikes regardless of what we've tried. After going through the process of upgrading the filter, adding beneficial bacteria, and simply waiting-and-seeing, we've ultimately decided that he may simply have outgrown his current setup, is kicking out more ammonia than the cycle is capable of dealing with. That, or there's something else in the current tank that's throwing things off. Either way, it's new tank time.

So! We've just ordered a Fluval Roma 125l. It's sold as a tropical tank and comes with a heater, but it's a separate component so we can just leave that out. It's due to arrive tomorrow and we want to get things set up as quickly as possible, but as we have the opportunity to 'start again from scratch' to some degree, I wanted to come on here to ask for some advice.

Cycling the Tank

Obviously, we want to get the cycle up and running as quickly as possible.

Using existing filter media - We currently have a Fluval U2 filter, which has two compartments for sponge media. We were planning to move one of the sponges into the filter in the new setup so there's some bacteria already present in the filter. Our cycle hasn't been stable in the current tank. Nevertheless, I assume this is still a good idea, or at least not an actively bad one?

Tetra SafeStart - Does this work? Is it axolotl-safe? I've heard mixed reports but it seems to be the most reliable of this sort of thing. The directions say to add the SafeStart, then add fish right away. I assume this is because the bateria you're adding need an ammonia source to thrive? Is it safe to add an axolotl right away after adding the SafeStart? Would it be advised to add a different ammonia source instead? Or none at all? Or avoid this option completely? Advice very much appreciated on this front.

LED Lighting

The new tank comes with an LED light strip built into the lid.

Axolotl-safe? I understand that axolotls are sensitive to light due to a lack of eyelids. I also am of the understanding that albinos are the most sensitive. Max is a wild type. Will the LED light strip be okay to leave on during the day, provided we include ample hiding places in the tank?

Live plants - We would like to add some live plants to our tank setup, which we've not previously done, as we understand this may also help to stabilise the cycle and cut down on nasties. So the LED strip will presumably be required to be on a certain amount of time for them to thrive? What's the best balance here?

Substrate

We are currently using a fine sand substrate. However -- ahem -- Max tends to do quite soft poos which he has a habit of immediately stamping on and trampling into the sand, making them difficult to clean up. We suspect this may be one cause of the ammonia spikes.

What's the consensus on omitting substrate? I have seen mixed things. Some say it's fine, and even preferable. Others say that A) the axolotl can struggle to grip the bottom of the tank, leading to stress; or that B) not using substrate gives the beneficial bacteria fewer places to colonise, leading to a less stable cycle. Any thoughts on these?

Axolotl-safe alternatives - If omitting substrate is a bad idea, are there any axolotl-safe alternatives that are easy to clean but allow for more of a grip? I saw someone suggest placing piece of slate on the bottom of the tank, which seemed like a decent shout...

Any other considerations?

Any other advice anyone would have on establishing a good, healthy, solid axolotl setup that will last for a long time? Max is only three-and-a-half so we hope to have him in our family for several years yet, and we'd like to ensure this can be a forever-house for our little slimy poppet!

If you have existing filter media absolutely utilise it. It will help the cycle a lot. It can either go in the filter or just in the tank.
The tetra safe start I think is just beneficial bacteria, you could use any brand and it should be fine. I use seachem's stability. Personally I wouldn't put the axolotl in until it's cycled if you can. It'll cycle in no time if you can do that as you wont have to do water changes.
LED is fine to use as long as there are a few dark hiding spots. I use one around 5-6 hours a day but my axies never seem to hide lol. You'll want to use a light if you plan to have plants, if you need any plant suggestions check this link, it also has other set up help https://www.caudata.org/axolotl-sanctuary/Aquascape.shtml
I usually use sand but I don't mind barebottom. I currently have juveniles so need barebottom but will use sand when they are older. It'll be much easier to clean if you don't have substrate. Some people don't like barebottom as axies can't grip on to it as well but I guess it depends on the individual axolotl. Mine don't have trouble without substrate but if you notice yours struggling to get around then add the substrate. You could also have mostly barebottom with some patches of sand in a corner. Slate is great for a base but I'd be worried about poop getting stuck under it where you can't see and you would need to take out everything to remove it. I've seen recently people using fake grass from hardware stores. It looks great and should clean fine if you use a gravel vac.
You seem to be on top of everything! Check out that link I posted, if you have more questions let me know