Additionally, use a heat gun (or even a hairdryer) to warm the connected stuck tubing. Heat expands the tubing, it may break the "seal" on the gunk in there.
Light taps with a small rawhide mallet or even a drumstick around the slide receiver may help but it's very, very easy to dent a slide. I wouldn't do this unless I was 100% sure of what I was doing.
Finally, instead of the wooden tool, use a leather belt. It does the same thing.
Remember, though, that it's not out of the realm of possibility for the slide to be stuck together firmer than the welds holding the slide together - especially if you're talking a lower-budget or lower-quality horn. Don't try to force anything you're not willing to have reconstructed at your own expense.