If you are planning to do a lot of surfacing in the future (and given your plans I would think you might) then the longer term solution is a planer; maybe a Dewalt 735 or something similar to that which is still about $500 - $600 depending on where and when you buy it. However, if you do buy one, be aware that you either must do the planing outside or find some effective method of dust collection. That is another expense if you don't already have a good, efficient dust collector. The amount of chips and shavings produced is huge.
Hand planing a large amount of wood is a big job unless that is something you have an interest in for skill development and need the exercise.
If you aren't going to do a lot of planing to thickness in the future, then I'd try to find someone who will plane the relatively small amount you will need for the project and decide later about the planer. Lumber companies who do custom millwork will plane. Some locally owned lumber companies who just sell hardwood will plane. Local hardwood sellers will definitely both plane, and sometimes, sand. If you have a local or regional woodworking club, you might be able to make contact with someone who will plane for you. Generally, the fees for planing are not that high and, if you aren't ready to buy the planer and accompanying dust collection, are probably your best option for a single project that you want immediate results on.