It's perfectly safe to take these intramuscularly if intravenous isn't feasible. If they truly are pharmaceutical Diamorphine then they should be completely sterile and viable by any parenteral or injection route, including Subcutaneous (under the skin), which really isn't suitable for your needs as it yields a protracted onset and duration, unless that's what you want. I'm sure there are more concise instructions somewhere on the internet, but IM is practically idiot-proof.
Prepare your shot just like you normally would. The less fluid the better for this route, but make sure you have an actual solution. Find a large muscle and grab it with your hand and feel around so you can identify just where it is. In medicine, the commonly use the Deltoid muscle to administer things like vaccines among others. I don't know if this is advisable, but I've always used my Biceps. They are easy to grab and identify, fairly robust and hidden from view; IM injections almost inevitably leave some kind of miniscule bruise or irritation.
I have almost completely switched over to this route. I still have veins too. One day I was in a public bathroom before work, sick and shaky, probably dehydrated and I couldn't find a vein. I said what the hell, grabbed my bicep and did the shot. I was surprised because I felt it come on with 1.5 minutes tops. I'd say 90% of effects hit within 5 minutes, with a small but steady increase to 100% up to like the 10 - 15 minute mark. Everything I had read had indicated it would take much longer. From that point on I just started sporadically going IM because it was easier and faster. Now I do it every time. I practice good hygiene. I was the area with soap and water, then alcohol, new rig etc. There are still risks, but it's up to you to minimize them.
So you're really not giving up much by going the IM route. Sure, you don't get the same rush, but once you hit that 1.5 minute mark, I really don't think you'll give a fuck. I didn't. Also, you don't have to sacrifice the bioavailability percentage that you would if you went for another route like insufflation.
As far as the Midazolam (Versed) goes, they are going to be best by the IV route, just like the Diamorphine, but just like the Diamorphine, going the IM route will probably be pretty intense and powerful in its own right. I've had about 20 surgeries in my life, give or take, and Midazolam is pretty much a given before any operation, like 15 minutes before they induce anesthesia and begin operating. Like you might expect, IV Midazolam is unlike any other Benzodiazepine that you would take orally. It's a pretty cool buzz. It gives me the same warm blanket feeling Opioids do to a certain extent. But, I'm sure IM'ing them would be powerful enough to give you a good buzz.
Be careful if you intend to combine the Midazolam and the Diamorphine. I understand you have a decent tolerance between the Methadone and the occasional street Heroin use, so you probably would be alright. 5mg of Midazolam is what I would typically get (I asked) and that's enough to get the warm, floaty, nice feeling I was telling you about. One time, about 2 minutes before they gave me the gas and put me out, they gave me another 5mg and I went totally goofy and was laughing my ass off.