That is some mapgasm. Second map seems very plausible but I want to wank on the first map so how and when would you suggest extending to the Vistula-Dniester (also extend to Dnieper and Black/Azov Sea as Roman lake?) if the Romans can't "borrow" infrastructure and institutions with little to no urbanization in these areas? Also hindsight is 20/20 so what compelling case would convince the Romans to go deeper into Germania and further east instead of Britain?
The point about hindsight is completely valid. Here are some ideas on how it could still work out in the intended way.
-- For Britain, I'd suggest a scenario where either Caesar's invasions succeeds in a more pleasing set-up of allied states, or one of the aborted invasions during the reign of Augustus goes through and yields such an outcome. The Romans secure the "Tin Isles" (Isles of Scilly) and and the Isle of Wight as a staging ground for military action in Great Britain (in case some local polity becomes troublesome) and as a secondary port for the fleet charged with keeping the local trade safe from piracy. This set-up means that direct occupation of Britain just never becomes required, since the existing situation is already sufficiently pleasing.
-- Also early on, Drusus doesn't fall from his horse, and carves a Roman client state of of Germania up to the Elbe. The Germanic elites benefit from their relation with Rome, and gradual Romanisation soon commences. Increased trade and interaction helps develop this part of Germania, compared to OTL.
-- As a side-effect, Drusus (who was favoured by Augustus) eventually succeeds Augustus. This prevents Sejanus from ever gaining influence (ideally, Drusus has him killed), and also prevents the reign of Caligula. Since Drusus was a highly capable man, putting him in charge is always a good start when embarking on a Rome-wank.
-- A further side-effect of success in Germania, combined with no (further) need to devote any attention to Britain, could be more Roman confidence in military expansion elsewhere, during the reigns of Augustus and Drusus. That is: get those ventures into the Red Sea to get a bit more support, leading to Roman trading ports established along the coasts there.
-- This in turn helps build an economic interest in the East. Presume that things develop largely as in OTL until the inevitable clash between Rome and Persia. Presume that some alt-Trajan still conquers Mesopotamia, but due to the greater economic interests in the region, it is decided to make that conquest permanent.
-- The inevitable Persian attempt to get back Mesopotamia must then be staved off. This will be very costly. If it is done, however, whoever's in charge of Persia is screwed. It was costly for them, too, but Rome has taken away their wealthiest region; their economic heartland. Rome has just won the big rivalry. Each passing year will now strengthen Rome relative to Persia, as Mesopotamian revenue flows to Rome rather than to Persia.
-- The next and final step in the east is to carve client kingdoms of out Media and Susiana. Since Rome is a distant benefactor to them, whereas a resurgent Persia would be a more near-by overlord, it's in their interest not to stab Rome in the back. This gives Rome a buffer to any invasions from Central Asia that approach via the Persian highlands. (Also, expand those trade ports to basically follow the whole coast of Arabia, so that Rome can safely move to and from Mesoptamia by sea.)
-- At this point, Germania up to the Elbe should be relatively Romanised and well-integrated. This will have had an effect on Germania
beyond the Elbe, which was sparsely settled woods and swamps in OTL. Benefitting from a developing region to the west, this area will probably be enjoing greater economic wealth (and thus a growing population) as well, compared to OTL. That will make gradual Roman expansion into the region (mostly by establishing small client states and then very gradually absorbing them piecemeal) more feasible. And also more necessary, because more numerous and powerful tribes across the border means more of a threat to your frontier.
-- I digress here into the fundamental operations of imperialism. There are barbarians across the border. They are troublesome. You sudue them and reduce them to vassals. Over time, they get more and more integrated into your economy and culture. As a result, they demand rights and protection... from other barbarians, who live across the
new border. You sudue those, too, and reduce them to vassals... repeat until you reach your operational limits.
-- With the wealth of Mesopotamia added to Rome's coffers, I daresay that Rome's operational limits can be pushed up to the Vistula, although at that point we're talking about client states that cannot just be annexed directly (too far away for effective control that way). Likewise, you can push your borders up to the Dniester and the Crimea. Keep in mind that Mesopotamia is a bread-basket, and that its surplus production can easily help feed an expanding population. Rome will have more people than in OTL, and will be able to produce correspondingly more legions.
-- Regarding the Black/Azov Sea as a Roman lake: I think a client state covering that area, basically covering the northern shore, is very possible. I am somewhat hesitant in this regard, however, because too much Roman entanglement in the area can lead to trouble you don't want. I've opted to go for what I believe to be the best defensive borders against steppe invaders. Note the successive defensible lines in the North-east. Dniester is crossed? Fall back to the Carpathians. Those get crossed? Fall back to the Danube. The point is to keep such an invasion from threatening the Imperial core at all costs. Optimising expansion is considerably less important than ensuring a succesful defensive strategy. Basically, I don't want the legions spread too thin. So an ally or client state north of the Dniester-Crimea-Carpathian frontier? Great. But expansion into that area? Don't do it. You can't successfully defend that area from steppe invaders anyway.
-- Once all the above is done, and assuming the geopolitical situation allows for it (i.e. no threats on the horizon), you can then start thinking about actual expansion into Britain, or into more firmly turning some allied North African peoples into clients.
