A bureaucratic class in the HRE?
Interesting Idea.
The big problem IMHO is indeed the feudal system, but as some already suggested, a short but brutal war might get rid of most of the nobility - like in France the battles of Crecy and the plague did within a decade.
With the nobility weakend and war a constant the HRE would have to rely more and more on mercenaries.
The best POD would be around 1500. There are the Hanse and the Fugger, both civilian organisation, both bureaucraticly organised.
(The Hanse was on the way out but still strong and the Fugger were at their height)
The Kaiser could see the opportunity - no nobles to tell him what to do but a functioning state thanks to more controlable civilan bureaucrats - strike a deal with them. Cities run with the help of the Hanse/Fuggers bureaucrats and under the direct control of the Kaiser. The now "ownerless" villages fall under the nearest city.
The still existing Aristocrats can either hide behind their walls until they as meaningless as the French nobility was, or they go for all out war against the cities and the Kaiser, which they will loose as the time of feudal armies was long over and they had no money to buy a decent sized army anyway. And this would mean the end of the feudal system in the HRE.
Over a relative short period, say 30-40 years, it could lead to a tighter bureaucratic controlled precapitalist state.
I do not think that absolutism was a possiblity, but a centralised state supported by a middleclass bureaucracy is.
However Marin Luther would ruin any progress unless the whole of the HRE becomes lutheran...which might actually help in centralising the state and increase support for the Kaiser among the lower class.