What you are calling a "pulley" is usually referred to as a "Block".
there is an old saying: "slow is smooth...and smooth is fast"
You might want to get a "sling" to go with it for attaching it to the tree. There are several kinds...I like a "loopie" they are easy for me me to adjust and set up..
The best way to get a tree job done quickly is to think and have a plan. Notice where you can save time and effort through efficiency. Make each movement count toward getting the job done as efficiently and safely as possible.
As an example: when you have just finished cutting where you are tied in and are ready to move to the next spot to tie in, see if you can tie in where you can make multiple cuts instead of just one.
Little thing like this, used through an entire tree, can save a lot of time and effort. If you watch most experienced climbers, they don't look like they are hurrying (they probably aren't), but they get a lot done through putting some thought into the job and saving as much effort as they can.
It helps save energy for those longer days too...
