If this doesn't work for you don't blame me but it worked for me so might as well share it. It requires you already have at-least one item in your Dispenser.TF library, if you don't it's tough luck, and it'll take about two minutes so it'll take slightly longer than normal.

Basically, first enable Anonymous buying on Dispenser.TF's settings menu (Should already be enabled if you're attempting to sell anything) then make a trade with the one item you have in Dispenser.TF's inventory and under the wishlist add what you want to deposit. Now, simply open a inprivate/incognito tab/another browser/logout and navigate to that trade, then do the trade via the Anonymous buying method.

This is *technically* against Dispenser.TF's rules (You get popularity for a successful 'trade' and attempting to cheat on the popularity status is agains the rules) so try at your own risk, but from what I can tell, Joto seems relatively chill (Reason why I've taken the risk) as to not go on a mass-banning spree.

It doesn't help people who have their items already stuck, but, it's useful if you need to deposit a few new items as the issue seems to be with the bot accepting the trade, not it initiating the trade.

Are you basically saying to start a withdraw trade to withdraw an item, and then add deposits to that same trade?