Toro
I left the UK military about 4 years ago with around 8000 hours, mostly C130. I applied to three airlines: British Airways, Virgin Atlantic and Cathay Pacific (Cargo). All were delighted to offer to accept my experience, and my feeling is that you would probably get a similar reaction - as long as you can find a company hiring just now!
4500 hours is serious time, and time on the C130 is highly valued as worthwhile preparation for airline employment. It is turbine, obviously (the fact that it wears props is neither here nor there), and I've no doubt you have experienced most scenarios the average airline recruiter can imagine - and probably a few more.
You are a very valuable commodity - but you are still competing against many airline-experienced pilots who have been made unemployed over the last 18 months. Nevertheless, I think you should feel fairly well placed. Good luck.