I would not get the BLM or the Forest service involved. They seem to like logging only at the bulldozer/slash pile/commercial level. For one or two trees it is going to be much easier to beg for forgiveness than to ask for permission. Also I am not sure on the size of the logs but you can cut through very large logs with a saw with a pretty small 18 or 20 bar. This is the type of saw that I use and I can get through logs about a 40 to 50 diameter log with a bit of work. Also if the logs are too big to be moved up on the bank make sure they will not get washed a ¼ mile down stream at high water and get hung up again.
I like to cut logs up into small blocks - like firewood and they should wash down stream easily without making another strainer. Also get the blade on yo saw sharp wet wood is very hard to cut through and if it is water logged it will be even harder - a sharp blade will do wonders.
Good luck and be careful it is hard to boat with only 3 fingers
. Also props for cleaning any run - Thanks for keeping it clean!