Without some screenshots of your wallet, it is hard to say for certain what the issue is... but the biggest clue for me is:
I usually process a lot of transactions and as time goes by there's BTC stuck on my wallets and the amount keeps increasing.
It sounds like you might be generating a lot of change addresses with dust amounts of change in them... as explained by DannyHamilton in another thread (which I can't locate right now)... given that fees are currently in the 250-300 sats/byte range... and each input will add at least 148 bytes to a transaction...
Best case (compressed address, lowest "recommended" fee rate):
148 bytes * 250 sats =
37,000 sats per input.
NOTE: If it is an uncompressed address used it could be 180 * 250... = 45,000 sats...
So, if you have UTXOs that are less than 0.00037000 BTC in your wallet... and your wallet calculates dynamic fees... it will probably tell you that you have insufficient funds to send them... as the fee required to send that input is equal to or larger than the input itself
Pretty much the only option is to manually select all the dusty UTXOs from your change addresses... manually set a fixed fee that is calculated to meet the 10 sats/byte (0.00010000 btc/KB) rule for ViaBTC... and consolidate all this dust into one output back into an address that you own. Then attempt to accelerate the transaction using ViaBTC and cross your fingers :-/