Also, winching a stretchered patient into a 135 looks like it would be a little tight (that's before looking at the performance limitations) and we were wondering how people got on.
You are right, it's a tricky operation but possible. But don't forget the 135 is a small twin and nearly all small twins have that problem. Therefore the crew decides if the helicopter have to turn to the next usable landing site or if the stretcher have to come into the cabin. And ... the procedure depends on the cabin interior. Most police and HEMS ships have a lot of interior like racks, seats, ... .
Woolf is absolutely right. Fixed line is a safe and proven procedure! Have made hundreds of fixed lines including really rescue missions. Most civil HEMS operators don't have so much rescue missions with the need of a winch. They don't need a winch, the additionally winch weight, the weight of the winch operator and his monthly costs. The police units doesn't have the same problem. Normally they have enough paid personal like technicians, FLIR operators or other missions specialists ready to arm the winch.
Austria is the leading EC 135 country with more than 20 ships in this small country. They tested the winch in the Alps but use today only the fixed line.
Air Zermatt in Switzerland holds a EC 135 with winch. But the ships is nearly empty for winch ops.
Short haul in tricky area is much cheaper with more possible performance, but needs much more pilot (crew) skills compared to winch ops. Therefore the operators have more training costs.
One other advantage is the greater load on the fixed line. In the Alps they lift up to 6 persons at once with the EC 135 (partial fuel)and fixed line for example on skilift evacuations.