"Troccupé" will not do, unless you pronounce a long o, that is an o that is nearly twice as long; it is better to pronounce two o’s with a small silence in between. Here is this second pronunciation with a small silence : audio.

You have the choice to make the liaison or not (tro-occupé, tropoccupé).

The difference between "Je’n sui pa" and "je ne sui pa" is rather a matter of regional accent : in the north of France and in Paris you are mostly going to hear the first whereas in the south it’ll be the second a lot.

I have never heard Trocuppé although in fast speaking, an untrained ear might be fooled.
The O need to be longer than a regular one, even if only slightly more, for the phrase to be natural.

In normal speed speaking, there is a syllable separation between trop and occupé. It can be thin.

Pronouncing the P of trop is also possible but more formal and rarer.

Je ne suis pas is indeed often pronounced je’n sui pa, better written je n’suis pas.

This isn’t "against the rules" as usage makes the rules as far as pronunciation is concerned.

Moreover, je n’suis pas is still on the formal spoken French side as the most common way to say it fully drop the ne to make either je suis pas or "chuis pas".

In good French, you must say [tro.po.cu.pé] and not [tro.o.cu.pé]. The liaison is an essential characteristic of the spoken French language. Though in the present day, with the cultural debasement, the liaison is often omitted, it is incorrect to do so.

We even add phonetic letters to create a liaison when we feel it is missing, as in the expression "va-t-en": [va.t(en)] the "t" here is only added to prevent the ugly proximity of "a" and "en".

Today, with the advertising industry, spoken French is deliberately damaged, as in ads you will always hear "vingt euros" pronounced [v(in)(eu)ro] instead of [v(in)t(eu)ro]: And still, noboy will ever pronounce "vingt ans" as [v(in)(an)] but everyone says [v(in)t(an)]: In the same way, everyone should say [v(in)t(eu)ro].

Though eminent writers told the advertisers it was a mistake to say [v(in)(eu)ro], they carry on doing it, because they think people are not smart enough to understand the liaison. I believe they are not smart enough to understand people are not as stupid as advertisers think they are…

I do not agree that the liaison is more formal and rarer. On the contrary, liaisons are increasingly prevalent, to the extent that you hear a pause followed by the last consonant of the previous word. Les étudiant…….s’en parlent souvent. The famous and erroneous exaggeration of this is quatre……semployés