Your Buddipole is not assembled correctly. The loading coils should be at the end of the large diameter rods with the whips connected directly to the loading coils. It'll work much much better that way, and the taps and tuning will be closer to what the instructions suggest.
Just brainstorming here.... How high is the tree? If a lot higher than your balcony I'd want to get a very thin 'random' wire high up in it ....or from that tree to another tree ...by catapult, bow & arrow, drone, helium balloon, highly trained monkey....an early morning stealth expedition while others are asleep. Pour fertiliser at the tree roots, as it grows you will eventually get to cover 160 m 73, jeff
And of course you have to try TAKTENNA .I prefer horizontal installation. Homemade.. it will cost about 20$...you can make it with bare steel wire 2mm (( NO COPPER wire)) and distance between the turns 5 cm ..And i use homemade voltage balun 4/1 on the antenna ,,On a aluminium mast 4 m above the ground...It gave me qso 20m band with YB0AR area 5/9 real report!!!! ,, 40m in Europe and local qso ,17m OZ ...5/9 https://ham.brugtgrej.dk/forum.php?mode=thread&obj=19380
Call Albert at ultimax antennas and see if he can build you a DX100 using Poly-STEALTH wire. Then put some string and a weight on the end of the wire and toss it into that palm tree. You can take it down easy, it will be hard to see. Much harder to see then what you have now.
The tree is about 50 feet and it is a palm tree. I can't put anything up on it as it is trimmed regularly
I am currently using an external auto tuner then MFJ- 939. I have been able to tune the bud dipole for 40 - 15 meter