As for the rest, I don't know where 4 German armies are going to go, presumably 150-250km from their starting points, also presumably one would go into the Baltics. I doubt the Russians will send the 9th army to Galicia, it or the 10th would go to the Baltics and the other probably to some blocking position in central Poland.
Neither the Russians nor the Germans are going to waste resources in the Baltics until decisive confrontations in Poland are resolved. The Germans were obsessed with decisive battles and battles of annihilation, so sending a significant portion of its forces into the Baltic wilderness in the opposite direction to Russian forces seems improbable. However, running down the remains of the Russian 1st army and liberating East Prussia might distract a German army for a week or so.
The Russians would likely be familiar with the Prussian phrase, 'he who defends everything defends nothing'. The Russian 9th and 10th armies would almost certainly be redeployed within Poland to fend off the German armies in East Prussia, but with the benefit of hindsight, those forces will not suffice to hold the Germans for long. When do the Russians fully recognize this danger and what do the Russian 4th and 5th Armies do? Without the Russian 9th Army, the A-H front would be more of an arm wrestle.
From a German perspective, I think Brest-Litovsk (from North/East Prussia) would represent a worthy and achievable goal for late September-early October.
IOTL the 9th Army took from 13 July to 30 Sept, 11 weeks, to travel some 250ish miles following the Russian 'Great Retreat', but that didn't start with a major battle followed by sieges of fortresses.
In this scenario the initial battles in East Prussia are likely to be relatively quick and decisive in the German favour, far less draining on German logistics than Gorlice-Tarnow. Maintaining logistics of an advance of 2 German armies in 1914 is far less onerous than the 13 CP armies supported during the great retreat. I also speculate scorched earth would have been applied more methodically in the somewhat controlled 1915 retreat than in a 1914 Russian rout.
Some thoughts on the early "Great Retreat" ITTL compared to OTL.
The russian didn't do that after Tannenberg, as well as not after 1st Masurian Lakes and the Battle for Lodz, which gives you a situation similar to what we have here already in ~ early Sepmtember.
The key differences between OTL are instead of one exhausted 8th Army, the Russians will be facing 3 relatively fresh German Armies in East Prussia. Instead of a recently formed/ forming German 9th army, you have a fully formed German army and trainloads of siege artillery. OTL the German invasion of France forced Joffre to temporarily adopt more sensible defensive tactics at Marne, so my thinking was the dire circumstances facing Russia might force the hand of STAVKA to deal with reality.
It's not a matter of
if there is an early 'Great Retreat', but
when. From a Russian perspective, the sooner the better. As an aside, how quickly could the Russian 9th and 10th Armies effectively re-inforce the Russian fortresses along the Narew river?