Many things to consider here but sounds a lot like a wound up neural issues down the effect side. If hopping up and down is fine compared to running then you have to think the hamstring and hip are potentially creating an issue.
Strengthen everything not just what physio gives you hence why seeing an S&C coach who works with runners who look at everything rather then just where pain is present.

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Andrew Garwood
http://www.2xu.com
http://www.newtonrunning.com
http://www.ascendsport.com.au

I’m dealing with a calf injury right now as well. Started a month ago, and same as you, I was trying to strengthen it (both soleus and gastroc exercises). I could jump up and down on it, and not have an issue, but if I started to run, I would make it a half mile (0.8km) and it would suddenly hurt again and I could no longer run. Saw the sports med doc yesterday and he did an ultrasound of my calf. I have a small tear at the myotendinous junction (where the muscle turns into the Achilles) and he believes it may take another two months of resting it before I can safely resume running again. You may be dealing with something similar so figured I’d give you my experience.

I had many injuries before and now I go to a specialist right away. I know when something is wrong, and a doctor mostly can't help it when something is so wrong I need to see a 'docter. So I see a specialist (surgion) right away. This is the quickest and best way to know what is wrong. And gives u the best treatment. Now u lost a lot of time by resting. While maybe something worse is wrong.

Based on my experience, with many calf issues, the wound is not yet fully healed. Needs more time. Keep doing rehab work. Ride your bike. Give your body the necessary time to repair itself. He will do.

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STRAVA INSTAGRAM

All good advice above, if i neglect ankle dorsiflection work for an ankle i injured many moons ago, my soleus will eventually talk to me, especially if i ramp up milage or speed too fast because I just feel good. Banded distraction of ankle plus calf strength and stretches are my go tos.

I have battled a similar problem off and on for years. For me, the problem is really with tight and/or weak glutes. I'd suggest working hard on your hips -- it's veery possible that the root cause of the calf issue is with your hips/glutes/hamstrings, and the result is the calf muscle over-working. Hope it gets better for you.

Cool thanks for the replies. I got 3 "runs" in this week all under 2km, and calf was OK.. will see how I go this week, and will work on hips glutes too.

Can’t help more than others have said but diagnostic imaging might be good - sounds like things are working better if you did 2k. Keep us posted , hugs

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maybe she's born with it, maybe it's chlorine
If you're injured and need some sympathy, PM me and I'm very happy to write back.
disclaimer: PhD not MD

https://www.pogophysio.com.au/...-strains-in-runners/

Calf versus achilles?
Go and see Peter Steele at Subiaco Sports Med. He will sort you out. Ex runner, ex Dockers and Hockeyroos team doctor. I love my physio's (and don't mean any disrespect to them) but sometimes you need a sports medicine specialist/specialist with access to more advanced imaging. As others have suggested, specialist review +/- imaging early in the scheme of things can be a better way to get to the bottom of the issue(s).