I like endgames, so this is a fun question. I've studied this endgame and I'm aware of the cochrane defense, the philidor position, and loli position.
But still, you're an IM. The average level of players on these forums is like... rated 1000. It's funny to me you post such an interesting topic on these forums and then ask for meaningful responses.
Chess.com forums are more of 8 year olds with pokemon avatars and sub-1000 ratings posting 1 word responses.
Well, any suggestions where to better post it? This site has a lot of strong players lurking around, so I thought it might be a decent place to start. And I could see players rated 1800+ having interesting ideas here.
Anyway, here is my initial take on the position, maybe that helps starting a discussion.
The (to me) obvious move to start is 1.Be5, intending to advance the king further and sometimes operating with Rd6+.
Now the move I find most annoying is 1...Rc5! because it enables Black to answer 2.Rd6+(?!) with 2...Kc7! without losing to any discovery.
So what I would probably try here is 2.Kd4 Ra5 3.Rd6+ Ke7 4.Ke4, planning Ke4-Kf5.
I think Black should answer with 4...Ra2 forcing the white rook to move away.
So let's say 5.Rh6 Kd7 (5...Re2+(?) would allow 6.Kd5 Rd2+ 7.Bd4 and White will achieve his goal) 6.Kf5 Rd2 and it's not obvious to me how White should make further progress. Of course, many alternatives were possible along the way.
You're right, you might get some good responses 
I was just using your topic to take some cheap shots at the forums. The forums are sometimes frustrating to me.
Yes, the forums (or fora depending how pedantic one is, and how this comment will upset some people!!) can be rather frustrating. But don't be too hard on people who have had no education through no fault of their own. Live and let live. For the ultimate in literary accomplishments, look at the daily Puzzle comments. I don't think.
Now for this exercise let's say white to move and if you manage to force black's king to the back rank for 3 consecutive moves, you win the game. Looking forward to your suggestions, feel free to either post whole lines or single moves and I will answer as the defending side.
No, it is impossible to forcibly cut the king off and achieve a winning game state.
By now, I suspect it to be that way too. However, it's strange that various endgame experts have claimed the opposite in their books.
Bc3 is a very nice idea, Wolf183! At first glance it looks quite promising. I don't have the time to thoroughly check on it now, but I will definitely revisit this idea tomorrow.
The idea/analysis after 6.Bc3 is quite convincing.
However, I found a new problem at an earlier point: breaking Black's defence if he simply keeps control along the 5th rank by e.g. 4...Rb5 5.Kf5 Rc5 (preventing White to go for Rc6-c7) 6.Rh6 Kd7. For now I haven't managed to come up with any ideas how to do so.
Now for this exercise let's say white to move and if you manage to force black's king to the back rank for 3 consecutive moves, you win the game. Looking forward to your suggestions, feel free to either post whole lines or single moves and I will answer as the defending side.