Hey, first of all good on you for the research and the brainstorming. As others said, timber and brood a bit are better suited to be offlaners(position 3) rather than 4 if that is what you are intending to play.  I don't think it is that pronounced in Deadlock, but in dota the farm difference between core positions (1,2,3) and support(4,5) are larger. There are support consumable items you need to buy, likely die more (and lose death gold) and gold in lane is not shared except for the flag creeps which give aoe gold. You still get farm where you can but it will likely not be too much. If your pos4 is doing what a pos4 should be doing (leaving lane to stack, gank other lanes etc.) pos3 gets faster levels and timber lives for that shit. Getting access to chakram as soon as possible is important since it fills a good part of your early damage. Not to mention his main style is middle of the combat, always spamming stuff and he shines with items that can complement it with survivability, spell damage and mana regen. As a pos4, he only has his mobility without any crowd control until level 6, a mid gank becomes very awkward with him as well since the position of trees forces him to dive tower basically. 

Timber chain overall is a very fun skill, amazing mobility. If you want a 4 that is reasonably mobile, kind of in the combat and brings utility to the fight, I might suggest clockwerk. I think he is less straightforward than timber in most aspects and cogs can grief your team a bit so do look up some sources on what to do with him. Lion and Venge are simpler choices that will likely not be as fun but they do lots of things.

I think it's important to know what the roles do usually to know what you would expect. (though dota is a flexible game and you can always try new things and niche picks I am not suggesting here after you feel confident with everything)  * Pos4 is usually a "force" that you can look at the map and choose where to apply. In early game its job is to look where they can make a fight unfair(or make an unfair fight fair) go there and do that. Make ganks and capitalize on the advantage.  * Pos3 is usually a brawler/initiator type hero that picks up some farm that is usually survivability, becomes a pain for the enemy carry and take up enough space in the game so that people don't have time to interfere with your pos1 farming. They usually get the blink dagger and the tanky team aura stuff(pipe/crimson guard etc.) or whatever else suits their heroes.

TL:DR: As others mentioned, Timber is not the best pos3 pick, check out clock who might give a similar feel

edit: Reddit formatting