Semaphores (not heliostats). Even a system that does not use lights can speed up communication from weeks to hours. One of the main destabilizing factors of the Roman Empire was military uprisings by army commanders; semaphore lines halve the reaction time, or cut it down even more since you can activate army rivals within hours.
Positional notation for numbers.
Roman numerals are horror for arithmetic. Only specialists could do it.
Our standard decimal system is one, and probably easiest to introduce. It is base-10, which makes it easy to divide by 2, and 5, and any multiplication of them; division by 5 isn't that interesting in practice, 3 is much more useful, so introduce base-6 or base-12 if the populace will accept it.
Child labor is common and a necessity for many. You have half a year between "you can talk with it" and "it is needed for field work", so use that time. The amount of knowledge you can pass on is limited; take your estimation of what you can cram into that time, then reduce it because children will break down if you overdo it. Remember you can't force parents to send their children to school.
Open those schools for adults, too. Deal with those who have knowledge to strongly oppose to that. Some will do anything to block the growth of unwanted competition: PR, slander, arson, murder, judicial system abuse.
You will have to budget for this, but distributing knowledge is the fastest way to get something into motion (also the most uncontrollable one - be prepared to deal with, erm, "inappropriate" use of the knowledge, that's a pretty good plotline generator).
There was no police. Robber bands were active within towns; the wealthy needed bodyguards to get home at night, the poor weren't worth being robbed, but the middle class had to stay at home or get robbed (so the middle class had a hard time doing anything).
Communities tended to organize a militia. Know a few strong men, pay them to pay the robber of the last night a visit and take back at least the one trinket that you really cannot afford to lose. Hope the strong men aren't paid more by the robbers last night (but most robbers cannot afford to give back too much). Those strong men were essentially enforcers, who might or might not ask questions before taking out their sticks - you chose your enforcers based on what you wanted to have, and you didn't want to escalate things so far that they'd simply slay you (robbers usually don't want to slay their victims: a dead victim can't be robbed again). So it was somehow manageable, just not really safe.
Separation of Powers.
Strengthen the police and see it abused by the powerful... so you need to install a judicial system. You'll need to invest it with some religious mumbo-jumbo.
However, the Romands knew how to apply rules "sine ira et studio", i.e. neutrality and objectivity were known concepts, you'd just have to make sure that it becomes the operating principle of the judicial system (the Romans tended to stick with "what works", not so much with "the principle of the thing", so you'd need a demonstration community).
Modern (sort-of) economics.
Get somebody to work on Adam Smith's theories, and translate them to the contemporary mindset. Should work well since Romans had a pretty mercantile mindset, but they were also pretty matter-of-fact with cartels and other forms of powerplay such as murder, so if something went too far they turned to interventionism.
Not sure about human rights, or emancipation.
The "patronus" was essentially king of his family. Females were always under patronage: Of the patronus of the house they were living in (whether his family or not), or of their husband when they got married. Independent women were almost nonexistent, and had to make a living by, er, "entertaining" wealthy customers (the smarter ones went far beyond just sexual entertainment, but even these were never equals to their customers).
Either accept it as a fact of the Roman culture, or risk strong opposition (in particular, senate starting to oppose you) trying to change it.
These changes take time. Adopt a policy of travelling to the future, see what worked and what didn't, travel back and adjust. If your time-travel mumbo-jumbo allows this.