Ok, first off, maybe not as bad as you thought. Actually this is the best time to get your plants done now. Any other time draining and starting over is a complete no no. A easy way to stop mudding up the pond is to put a layer of clean pea gravel or larger if your planning on Koi on top of your planting media. I use a small layer of pea gravel then top it with larger river rock. First this keeps the dirt or kitty litter or what ever your using in the pot,(BTW, I recommend against using dirt, or bagged planting material that is designed for house plant use) second rocks in the top of the pot makes it harder for the Koi or other fish to dig in the pot once it is in the pond.
Planting media I do recommend using, Aquatic plant media, available at most places that sell pond plants, also can be found at some Lowe's and home depot. 100% pure clay kitty litter, tidy cat. works great but needs to be thoroughly rinsed or it will cloud the water! We have a dealer here that highly recommends using river sand for planting media, For lilys it works great and it doesn't mud up the pond nearly as bad, but again with koi you have to put something where they won't dig in the pot. River sand, must be clean and of a known source that it is safe, ( My dealer actually recommends cooking the sand at 300 degrees for one hour to kill anything in the sand that night contain parasites or bacteria) Do not use playsand or sand for mixing with cement, It's not the same and it doesn't do good at all! Pea gravel itself also works good for plants like Taro's, Pickerel rush,Thalia, Iris's and such as they will grow their roots out of the pot and it gives the fish a place to lay eggs and young fish will use them for protection.
For Lily's I recommend using pots that do not have holes in the bottom, a cheap pot is buying new oil change pans, the low profile works great for them and they can be found at dollar stores for about $2 each. Plants that are marginal I prefer using aquatic plant baskets, the roots can grow out through the basket
Now for the pond, If your going to drain and clean and start with sparkling clean water, This is the time to get the plants in place, do all your decorating then make this the last drain. Once you have started with fish and cycled the pond this is something you DO NOT want to drain the pond. Stirred up sediment and particles will settle and clear up in a well planted good filtrating pond. In most cases that should only take between a day and a few days depending on how well the pond the pond is filtered and how established the plants are.
I always suggest to fill the pond, wait 24-48 hours to allow the temp to settle. Be sure and use a good dechlorinator. get your ph and GH and KH set. This is easy to do when you have no fish and new water. Once fish are added everything needs to be adjusted very slowly. Ok, now your water is filtering, all your water checks come in good. Now is when you want to add some very inexpensive fish. I recommend using regular goldfish. They are hardier and this is going to be a hard time for any new adds. Koi do not do well at this time. Now wait, and monitor for ammonia, Feed very lightly maybe once a day during this time, In most case it takes about 4-6 weeks for the pond to cycle. When it starts to cycle you will start reading ammonia on your test kit, it may get kind of high, It's normal, You'll start seeing the ammonia go down after several days, start testing for nitrites, they will climb high and then drop down. Once this all takes place then the nitrates will start showing up. this means the bacteria have now caught up with the fish load in the pond. start feeding the starter fish more. Pump them up and feed them small amounts but two or three times a day. This makes them poop more, the more they poop the stronger the filter system gets. By this point your pond should be about 2-2 1/2 months old. now you can start adding choice fish. If you will only add two or three once every week to two weeks it will allow the filter to catch up each time to the new fish load. I highly recommend quarantining any fish for at least three weeks and four would be better before adding to the pond, this give you time to fully inspect the fish, if something shows up that they are sick or have disease you can treat them in a smaller area and not contaminate your pond. I've used this technique for many years and have helped many people start their ponds with success. there are other methods for sure. to me this is the most simple for new ponders. Remember these two tips. Patience is a key, don't get in a hurry adding fish, don't make drastic changes, always take baby steps and you'll be fine. second and most important. Unless it is an emergency and you have to do something right then, wait and ask someone before assuming you need to do something. Don't drain the pond, don't medicate, don't start using additives that are suppose to fix the pond right off, take the time to find out for sure if what your doing is right. 6-12 hours of waiting for an answer might save you $$, heartache and lots of labor that was needed to done. Plus, your fish will far more likely to reach a ripe ole age. Hope this helps, good luck!