I really like the concept (what can I say I'm a sucker for the Beowulf references), but I'm not really sure on the execution. This sorta makes all armor kinda unusuable if you have low strength; if they have a strength rating of +0 to start then a rogue who relies on dexterity but took strength as a dump stat cant even wear leather effectively. Further, it seems a bit complicated to figure out how ones strength influences each suit of armor.
The current rules, relying on armor proficiency and the physical weight of the armor to be a deterent for those of lesser strength, are kinda in the flavor of the beast we're talking about; but those are so easilly solved... how's this? Another weight catagory above heavy armors. I dont know what to call them, superheavies or something. These armors have high armor bonuses but are initially extremely limiting. However they grow less and less impeding as your strength increases until reaching some sort of maximum or running out of mobility to unimpede.
A hypothetical example, these numbers are drawn off the top of my head and therefor have little grounding in balance yet
super heavy armor, ac bonus: +14, max dex: -5, acp: -14, weight: something high
A player with 10 strength or lower would be effectively imobilized, or at least would have a dexterity penalty to ac that makes them look it. however, with every like 1 or 2 strength bonus they have, the max dex increases by 1 and the acp goes down by 1. At 30 strength they no longer take a penalty, and at higher and higher they can move more and more and start showing off and doing cartwheels or something. When theyre at a penalty to max dex it could apply to everything that uses dex, ruining their initiative and saves as well.
Aside: i liked the strength to move speed idea. That was pretty cool. Should use that with the superheavy armor.