If you have koi in your pond then it is a koi pond. I think you are saying that it isn't a 'koi' pond because it doesn't have a traditional filtration system used for koi.
Are you tired of having to drain the pond and clean it out? Then...
YES! Bottom drain all the way. It is a little scarry cutting the bottom of the liner, but if done right then no worries. You need to get on a koi forum called www.koiphen.com
Awesome site with MANY helpful people. They can help you with filtration design and many of them can help you build your own DIY filtration system. I don't think you have too many koi for that size pond so you are probably ok there.
As far as general design goes you typically go for a gravity fed system. Water always finds its level so that is what you are going for here. Not to mention if you can gravity feed it then there is much less disruption to the crap you are trying to take out.
I recommend www.koiphen.com
to ANYONE building ponds of anykind. You can bet that even if I had a pond without koi I would still have a bottom drain.