Is an X11 miner really necessary for that? Isn't there a way to lower the difficulty?
The main problem isn't really the miner itself (if you run your own private blockchain, the diff should be low, since you're the only one mining, so cpu, gpu or asic should all be sufficient). The main problem is that you're cloning coins that are old (like bitcoin and litecoin). The developers of these coins removed a lot of code that was no longer usefull because these coins have such a high hashrate it is no longer feasible to do solo mining, or start mining from your wallet (setgenerate true) or from your node (gen=1).
If you end up cloning a mature coin, it is pretty hard to solo mine the first blocks, since things like getwork and even stratum were long removed from the sourcecode of your mature source coin... So if you want to solomine a coin that is cloned from such a mature coin, you basically have to set up a complete pool, otherwise it will not work.
Agreed in some aspects but actually a lot of altcoins that you see these days have the built-in miner edited out but you can still use standalone miners to solo mine, you'd be crazy to use the built-in ones anyway