I will give some impressions of my play, although it is not a real guide. I'm also still in the early times for some reason, around 1240. Be graceful with my English.

I started a campaign on H/H and stopped soon because I didn't disabled the moves of the AI on the campaign map which is boring and stressing in the long term. Then I started a campaign on H/H again and soon a second parallel campaign on M/H to see the differences. In the M/H campaign I gave HRE a huge starting treasury of 30.000,- G and increased the kings money from 1500,- to 2500,- a turn.

Speed is your friend in the first turns. You get an army near Hamburg (rebels), hurry it to the castle immediatly, otherwise the Danes will siege it the second or third turn. After the fall of the castle you can build a harbour; as in MTW and RTW sea power seems to be the key for victory in the later game (just my experience). If you are a German or know something of the geography (or both) you can also get a little annoyed at the location of the harbour which is on the shore of the baltic sea instead the north sea. And why Hamburg is a castle and not a rich merchant city only CA can tell.

You could also try to get Antwerpen at an early stage which would offer you big money and a harbour at the north sea, but I would not recommend this. The rebels inside are fairly strong. But worse, it brought me in conflict with France in my first campaign, something I wished to avoid at all costs.

In the actual campaigns I ignored the flemish coast. I was never attacked by France with was a bit surprising considering the experience from MTW. But there are other attackers left.

Second aim should be Prag/Prague/Praha. You get order from the council to catch Magdeburg, but Magdeburg is a small castle and what do you want with another castle? Also Poland seems to be scripted to attack Magdeburg, which can cause conflict at an (too) early stage. If you want to take Magdeburg, hurry up because the Polish go straight to siege the castle.

After Hamburg and Prag I took Stettin on the baltic shore (annother castle unfortunately) and transfered it in a village. Fourth was Metz (a castle again) then I stopped to consolidate my robbed land. I transfered Staufen, Metz in towns at the first opportunity.

From the beginning HRE is the strongest power in the world. Haha. It's a power desperately in need of money and money is everything im TW games. I reduced troop production to Hamburg (castle), Frankfurt (city) and Innsbruck (castle). I really developed only Frankfurt and Hamburg for the military. Later buildings cost a huge amount of money, money you need for your troops instead.

You now have ten provinces but you need many troops so you never have enough money. So you need towns and farms and markets. Spend every money for economical growth. Selfexplanatory. And building streets is now essential. I'm a defensive player and I never managed it very well to have enough troops but not too much troops. You can come into depth rather easily if you produce too much because of the ever increasing danger beyond your borders. More later.

I don't like the pope and I never built up churches at a great level. That was not a very wise decision. Inquisitors began to wander through my countries. Oddly more in the M/H than in H/H where I rarely saw one of these frightening guys. In M/H till now they killed every male member of my family except for two. I like my generals and was not very pleased with this. So you should do everything to please the pope, building churches early on and obey every papal order.
I choose another way, now killing every inquisitor I see on the map. That is very difficult because of the low killing chances of assassins. You should do better and cringe before the pope.

The big problem of HRE: first everybody likes you (except the pope) which changed later on. In the H/H every neighbour came and signed treaties with me. I get Poland, Venice, Hungary, Milan and Denmark, Sicily as allies (and also other nations far more away), only France refused it. But that means nothing. Later all of the lovely neighbours attacked me except France and Hungary. Strangely in the M/H it was much more difficult to get allies. An explanation could be the fast building session I could start because of the large funds of money which makes me very strong very early. Something the AI nations do not seem to like.

Problems started for me from the 25th turn on. Suddenly I was attacked by Venice, Denmark and Poland at the same time. I survived only because of the sometimes very dumb AI. Interestingly it was not a great difference in the H/H and the M/H campaign.

In my experience you can do nothing to live in peace with the surrounding nations. I tried it and got my ass kicked. Therefore early offensive play is recommended I fear, something I don't like. First you should get rid of the Danes who have only one province. In the early game you can afford excommunication (only effect is +20% unrest in the settlements but that is nothing). Don't fear inquisitors, they came independent of being excommunicated or not. But in the M/H they left my country after I got excommunicated (strange cowards). After Denmark secure the rich and safe lands of Sweden, Norway and Finland. Next candidate is Venice, giving rich money, best defensive position and a bridge to your italian settlement at Bologna. The AI is not very clever so don't fear the battle at the bridge to Venice. Then beat Poland. After that you have to face France or Milan. In my M/H Milan is the superpower. I became their vassal many times with brought me some needed money and made me survive the struggle till now. You should attack Milan and later on Sicily wether you got excommunicated or not. I'm now at this stage, on turn 80 or so, you should do it as early as possible.

In the summary I don't see a big difference between H/H and M/H. The other nations are generally less aggressive in M/H, some rarely ever fighting others but the most aggressive are unfortunately the neighbours of HRE. M/H oddly was indeed harsher than H/H: without the cheated starting money I would not have survived some attacks. One interesting thing I found was that in the cheated M/H campaign the rebels had very good troops early on, much better than mine; maybe the AI choose troops by the level of the player buildings?

Perhaps I will write more when in the later HRE campaign which I deserved very much but meanwhile I started a Spanish campaign and that is far more fun than playing HRE in the early times and less danger to get additional grey hairs. And I think the later game will be very similar for every catholic nation.