That's the annoying part of reaper,
I can't help you right now as I dont' have a project of that sort but you have to play with the "set project timebase to :" and I think that would be "set to : beat" there are two choices, one including length+position+rate. This will ensure everything is sticked to beat positions instead of being recognized as "start point + a length". Otherwise, for example, when you change a tempo marker, objects don't have their end follow the change but stay the same TIME length. Even region markers, which is exactly what you don't want normally.
Then solution : create a Region for each block including a song. One done, try rearranging them but dragging the Region blocks on the very top of the timeline track on the top of your main editing window. I am not too sure about the comportment of regions regarding tempo markers for the different timebase but i'm guessing it's better to have it in beat mode.
Other solution : try cutting + pasting the whole song parts. Would be easier if you create regions since by clicking on a region you select everything inside.
I just tried in a blank project, moving a region around conserves my tempo markers at the correct time. And it automatically creates tempo markers of the tempo in the beginning of the region where it was initially placed after I move it right, and a tempo marker for the tempo of the end of that region if I move it left, so that the surrounding areas keep the same tempo. Now if the project or tracks timebase is set to a correct choice, the items should keep their relative positioning.
If the whole project is completely divided with 1 region per song starting with its own tempo marker (I suggest you create a tempo marker for the beginning of each region EVEN if the tempo hasn't changed since the previous song because you need that information kept into the region when you move it around and it makes things more in control) you can move any region before of after any other one without annoying blanks or tempo markers created anywhere. I just recreated that in my case and it works like a charm. This is also a method to be used inside a song if you wanna play with its structure. I'm not sure there is a playlist like in cubase or protools as I have never used the feature more than that.
You can then use the regions to export songs one by one in the export manager.
Forgot to mention, be sure you have Snap Enabled (the grid magnetism) so that your cursor selection always sticks to your grid.
EDIT : I just discovered under "Help" there is a special line about project timebase, you should read it quickly to understand the differences between the 3 options.
