There are many reasons why this should work under the way the rules are written. f it is not supposed to work than the rules need to be rewritten. I suggest changing the Dump Off to say "any player up to 3 squares". No way to argue how far you can throw then.

Now for the reasons it should be allowed.
1. Dump Off states you are allowed to throw a Quick Pass worked out as a normal pass action. Strong Arm states that you reduce the range of a pass by one band. Therefore, "a long pass is treated as a short pass", or in our case a short pass is treated as a quick pass. So what was a short pass is now called a quick pass which meets the criteria of a dump off.

2. This ties in with the first point. All the actions in Bloodbowl have the same procedure: declare, modify, roll the result. In a block, for example, you first declare the block. Then you may modify your ST with skills. If you roll a successful dauntless roll against an ogre your ST is then treated as 5. AFTER that, then you compare ST to determine the number of block dice used. A pass action works the same way. You first declare the pass. You may measure to any square you like. Strong Arm allows you to modify the range ruler itself making a short pass now a quick pass. Then you look up the modifiers to the roll and toss the die. I should think that if you are using the "+1 for a Quick Pass" modifier, the pass itself is considered a quick pass.

3. Not being able to use strong arm makes this trait inferior to accurate and usually traits are better than skills. It is made inferior because accurate gives a +1 on all throws, while strong arm gives you +1 only on 3 of the 4 types a passes. Not being able to use strong arm also reduces it to just being another form of the accurate skill. If all it does is give you +1 to throwing, then strong arm and accurate are nothing more than "stackable" modifiers. It would seem dumb to have this since you are not allowed to add together modifiers with any other skills (such as claw and mighty blow).

4. Common sense states that a strong arm = a strong toss. If a long pass is nothing but a short one to you, then wouldn't it make sense that lobbing it a few extra squares is just as easy?

I will just restate what I said above. If these two skills are not allowed to work together, it should be stated in the skill. Just as multiple block says it doesn't work with frenzy. However, I think the skills should be allowed to be used together. It only makes sense, and with Strong Arm being a trait, it won't happen that often. Is there any good reason why they should not be used together? Other than the "because we said so" excuse?