The Latin word is "quatenus", which my dictionary translates as "how far, to what extent; in so far as, since". Do you think "tiel, kiel" would work better than "tiugrade"? Esperanto constructions often have less "figurative leeway" than ones in English, so I sometimes can't tell what would be appropriate. Here's Definition 8, Part One for another example:

"By eternity I [mean] existence itself, insofar as it is conceived to follow necessarily from the definition alone of the eternal thing."

Could you use "tiel, kiel" here, "tiom, kiom", or "tiugrade", or all three, any why?

Whilst 'tiel' is only an adverb 'tiom' can be both a noun and and adverb. Mi ne volas tiom - tio estis tiom dangxera ke

Turning 'tiomgrade' into a phrase we get 'en tioma grado' - not 'en tiom(e) grado' or 'en tiom grado'.

'Stacidomo' and 'bushaltejo' might be analized as 'stacia domo' and 'busa haltejo'. But even if that analysis is faulty, by what rule in Esperanto can't you combine noun-roots?

Anyway, for me, Dark Weasel, there is clearly a useful difference in meaning between 'tiugrade ke' and 'tiomgrade ke' - isn't there?

sudanglo:
Turning 'tiomgrade' into a phrase we get 'en tioma grado' - not 'en tiom(e) grado' or 'en tiom grado'.

IMO this is dubious since tiom is a vorteto in itself, so it’s not very natural to interpret it as an adjective when it’s the first part of a compound.

sudanglo:'Stacidomo' and 'bushaltejo' might be analized as 'stacia domo' and 'busa haltejo'. But even if that analysis is faulty, by what rule in Esperanto can't you combine noun-roots?

These are another type of compound. PMEG distinguishes kombinoj like stacidomo and bushaltejo from vortigoj like tiugrade or anglalingva. I suggest you read through Vortfaraj principoj.

I think we can comfortably leave the grammarians to fight among themselves as to whether 'tiomgrade' is a vortigo de frazeto or falls into some other category of compound word.

These categories (as listed in PMEG) are very much a post hoc analysis of the application of the fundamental principle that Esperanto admits the simple combination of roots, where this is useful and intelligible.

The fact that 'tiom' is a free-standing root doesn't seem to me to be of much relevance with regard to the admissibility or otherwise of a compound.

I'm not even sure that 'tielmaniere' violates any rule of combination. I would probably not use it myself, but if it conveys a nuance beyond 'tiumaniere', tiamaniere' and 'tiel' then it seems justified.

By the way, notice that we say both 'tiel' and 'tiele'.

'Tiomgrade ke' seems to me perfectly to capture the idea of 'to the extent that' or 'in so much as'.

If I understand the argument that has been given for rejecting 'tielmaniere', then in the same way you should reject 'prilumi' since you can't say pri lumi as two separate words.