- Allowed
- Sound weird
- Incorrect
The above list comprises the key elements of your question. They will become the basis for my three-part answer.
ALLOWED
As we used to say when we were kids, "It's a free world!" Meaning: I don't need someone telling me what to do or that I'm not allowed to do this or that.
Well, it is a free world. Consequently, you are free to structure your sentences any way you like. Just be prepared to deal with the consequences if what is allowed turns out to be injudicious.
SOUND WEIRD
How weird your sentences may sound is very much audience dependent. Personally, I think the conjunctive adverbs you mentioned (viz., moreover, in addition, furthermore, additionally, and besides) would sound a bit stilted if used in a casual conversation with friends. While defending your dissertation before a group of advisors, however, the words might carry a certain gravitas and formality which would not be out of place.
In fact, audience, occasion, and purpose all determine whether or not a locution sounds weird or not.
CORRECT
Your choice of words and the punctuation to go with them is perfectly correct. More important, however, are allowed-ness and weirdness.
CONCLUSION
Personally, when I am deciding how I should structure my written sentences, I read them aloud. If they sound "hinky," I simply reword them. Sometimes a moreover just sounds better at the head of a sentence. Sometimes it sounds just fine in the middle. Along with how the word order sounds, the biggest factors, I believe, are the audience to, the occasion for, and the purpose of your sentences.