I grow my Monstera deliciosa as ground cover as well let it grow up on a large tree. It like to grow in places where it gets good amount of sunlight for fruit production. In this video you will get more information of what I mean by good sunlight.
https://www.youtube.com/watch?v=fpaYcdb4bN0In this video explain both Monstera deliciosa and Monstera borsigiana are vines and it can be climber as well as crawler.
https://www.youtube.com/watch?v=RXXGPS2oICcyour plant in photo show it is growing direction of the light which is somewhat its growing away from your avocado tree. It is good that you don't let it grow up your tree. I let my grow up big trees but in check. I don't let it grow wild out of control. As long you have space, soil with good nutrients, light, air circulation...etc. elements of what both of your plant's needs, then no problem if they grow side by side.
Make sure you grow the correct Id Monstera deliciosa and not Monstera borsigiana. Don't waste your time with Monstera borsigiana for fruit production. Here are reviews fruit taste of both varieties.
Taste Test Monstera Borsigiana Fruit Vs Monstera Deliciosa Fruit.
https://www.youtube.com/watch?v=taJRWbNyccYTaste Test Monstera Borsigiana Aurea Variegata Fruit.
https://www.youtube.com/watch?v=omIhMgFtipwMonstera Borsigiana Albo Variegata Fruit Taste.
https://www.youtube.com/watch?v=yucIGIkITA8When both varieties Monstera deliciosa and Monstera borsigiana young, they look somewhat very similar. At the time they mature, then you will note the differences between them. This video show both varieties were collected and grown from seeds by me.
https://www.youtube.com/shorts/5aRjG9xFZ3AMore video how you ID them.
https://www.youtube.com/watch?v=sBprGjzCSGgMore than one way to ID them. However, one of the most important keys is the "ruffles" . Mature Monstera deliciosa has large waves on the back of its leaf where petiole joint with leaf. This video would give you some examples when it shows "ruffles"
https://www.youtube.com/watch?v=_xkcJOtwbckMy question is when you said, "I bought as a small quart size tissue culture start". Most of the time green form Monstera deliciosa seedlings sold were grown from seeds. Where did you buy it and how do you know it was tissue cultured plant?
How old is your Monstera? Did you make any propagation from it?