How is it even possible to form Prussia from Austria without going into very deep gamy way ? Seem like a logical nightmare to me for would basicly have to go conquer quite a few territory of proper culture, get core on them, switch capital, switch religion to protestant, lose your Austrian possession, switch culture, conquer require territory and get core on them. God that sound like a freaking logistical nightmare.
Also add to that you will risk to be disliked by HRE province for that mad conquering so don't think you will be able to keep HRE crown without vassalising most voter.
I believe it is doable, and worthy of the pain if you take the austrian national decisions before switching. The "fast reinforce" austrian decision pair splendidly with the "high discipline" prussian one, making your army a 24h mobile slaughterhouse. And I am not considering what the austrian diplomacy and inflation bonuses would do to prussian war-waging capacity...
You do not need to be protestant to form Prussia! The religious requirement only applies for Brandenburg. In fact, there are three "form Prussia" decisions, one available only to the Teutonic Order, one only to Brandenburg and one to every other nation with primary culture either saxon or pommeranian. For the latter, you just need to wait until the reformation happens, you do not have to convert.
The easiest way to form Prussia as Austria is to conquer all and only the saxon provinces (possibly not all of them are necessary if you resisted the urge to grab the two austrian gold provinces of Aquileia, but hey, why not?), and build workshops only on them, but not on your original austrian provinces (yet). This should be enough to make saxon your dominant culture after you move the capital to a core saxon province, without selling any of the original austrian provinces. This may take around 70 years. Then you quickly grab the prussian provinces before the TE reforms into Prussia, wait 50 years and can change.
One warning: Bohemia has two saxon provinces with cores on them (the two Lausitz). If you don't take them soon enough, they will likely be assimilated into czech. The same happens with the austrian gold provinces of Aquileia, they tend to assimilate into italian pretty fast.
The biggest nag is that it forces the expansion of Austria to slow down, at least in the beginning.
It is not really a bad thing, you can steer Austria into a trading nation in the mean time - which can really help in achieving early the "monthly income" required for the Fugger decision. Moreover, expanding your economy can offset the inflation threat you have because of your gold mines.
About the HRE, if you plan to conquer Germany you don't want to be emperor actually! It would kill your prestige. Of course, you can be emperor for a while, especially if you vassalize Brandenburg (after stripping it of three saxon provinces) and Saxony.