Contract Employment & Visa/Perm. Residence

So I’ve been a 正社員 at a graphic design company here in Japan, but I am very unsatisfied with the work environment. I’ve had an incredible offer for a 契約社員 position at a great company, with completely flexible hours, great pay, short commute, etc. The position will be available starting in July, and if I want it, I would have to start then.

HOWEVER, my three-year working Visa is due to be renewed in January 2019. I also want to apply for Permanent residence status in 2020 (as I made highly-skilled professional status in 2017).

So I have a couple of questions.

(1) Will taking a 契約社員 position affect my Visa renewal process if they are willing to sponsor me?

(2) Will taking a 契約社員 position affect the likelihood of being granted permanent residence status in a year and a half from now?

You immediately lose the highly-skilled professional status if you change your company. With that type of status you're tied to a particular company (its name is even stamped to your passport). If you decide to change jobs, you have to reapply for highly-skilled professional status again and they'll count the points again.
Otherwise, it doesn't really matter whether you're 正社員 or 契約社員.

My reading of the HSP process is that you need to comply with the requirements of the programme continously between review dates. If you change your status, and still meet the points requirements, then you might still be covered. As in many cases like this, get professional advice and do not rely on an internet forum.

AlexanderStankov seems to be correct.
http://alba-international-as.com/cat-p1/%E5%9C%A8%E7%95%99%E8%B3%87%E6...
在留資格「高度専門職」の外国人が転職したら、
転職した場合には「高度専門職」の在留期間が十分に残っていても、再度在留資格を取り直さなくてはならない
もし、新しい職場でも高度人材ポイントが７０点を超えるのであれば、在留資格「高度専門職」を再取得（厳密には、在留資格変更となります）し、もし７０点に満たない場合には、「技術・人文知識・国際業務」といった在留資格に変更します。