How can I make trees with custom blocks but growing in a default biome?

Use structure to achieve this. Use biome structure spawning limit.

Also, if you want to choose a specific place (like a beach, dessert...), create a plant and put in the procedure of the ticks something to spawn a schematic. There put the schematic of your tree and finished.

Dont worry, i think with events you also can do it. 😄

Bananarang, structures are probably the most simple thing to do. Here is how to do it on a Mac:

1: Open Minecraft 

2: Do /give 'playername' minecraft:structure_block

3: Create your tree

4: Place your structure block and set the boundaries

5: Export the structure (tree)

6: Out of minecraft, do command space, then type ~/library

7: Locate the application support, open the minecraft folder, and open the worlds folder

8: Locate the world you built the tree on, and find the structures folder

9: Relocate the tree file to somewhere accessible

10: Import the tree into mcreator and do with it as you wish!

No problem. Just realize, there are thousands of tutorials out there, don't hesitate to take advantage of when someone is offering their knowledge!