How can I make my far away command blocks work

Put them in the Spawn Chunks

The Spawn Chunks are a 16×16 set of chunks centered around your world spawn. These chunks are loaded at all times, unless no player has been in the overworld in the last 60 seconds^*.

While some mechanisms are not processed when no player is around, such as plant growth or entities, redstone and command blocks are executed normally.

^{* According to the wiki. However, I have not been able to observe the unloading of the chunks on 1.8.7 in a singleplayer test world. IIRC SP is functionally identical to MP.}

The only option would be to tell the player to set the render distance to at least 13 chunks. This will make sure the Command Blocks stay rendered, and allows them to execute commands. Here is a list if you've placed any command blocks further than 208 blocks:

Source

Another thing that may interest you is make a downloadable texture pack, and change the texture of the command block and whatever else you are using to something like dirt. That way the player has no way of knowing that what they are standing on is a command block, unless they switch gamemodes.

I just came up with an idea.
Place a singular command block somewhere where it can be triggered, have some way of triggering it, (via redstone, for instance a pressure plate directly on it, or to prevent players from seeing it, have said pressure plate triggering a trail of redstone dust which then triggers the command block), and set the command to

/setblock X Y Z redstone_block

Just for clarification, for the X Y Z values, set it so that the coordinates are the same as the command block(s) you want to activate, but change one value to be one less or one more than the actual location of the command block, as to not accidentally destroy the command block you want to trigger.
I hypothesize that a lit redstone torch can serve the same purpose, just make sure that it is placed on top of the command block you want to remotely trigger (also, to use the redstone torch instead, put redstone_torch in the command prompt in place of redstone_block).

From there, make sure you have the commands for command block or command block chain you want to activate, and if I've done my thinking correctly, the newly placed redstone torch or redstone block should activate the command block regardless of the player's location. Then, to allow for the command block to be remotely triggered again, make sure that there is a second command block in the first chain (the one you are using to remotely trigger the others that are doing what you want to be done), and make it replace your newly placed redstone torch or redstone block using the command

/setblock X Y Z air

or, just for good measure to ensure the redstone block or redstone torch is removed

/setblock X Y Z air 1 replace

Make sure the coordinates set for that second command match the coordinates of the redstone block or redstone torch being placed, or else it will either do nothing, or remove something else entirely.

I have yet to try this, but will immediately after posting this answer.

EDIT:

I just found out that I can edit these, but IT WORKS. IT ACTUALLY WORKS. I was trying this because I wanted to make a story-based adventure mode zombie apocalypse map using someone else's zombie apocalypse store packet thingy on the PS4 Minecraft Bedrock store, and needed dialogue, but didn't want command blocks getting in the way, but I tried it, and it legitimately works! I had thought of the idea in just a couple of seconds, and generally these sorts of quick ideas of mine don't actually end up working in practice, but this one actually does! I REALLY hope this helps, as it sure helped me!