Adam
You could have a look at the following forum
http://www.yetizone.com/wwwboard/wwwboard.htmwhich is exclusively about trekking in Nepal and the EBC in particular. Bear with it since there are lots of weird people posting on that forum. But they also speak Australian

Also check out
http://trekinfo.com/forumswhich again is specifically for Trekking in Nepal but I suspect the moderator blocks the rubbish post.
EBC is pretty easy, well marked trail, loads of trekkers. If you can walk 15Km with a 5Kg backpack in the bush on fairly roughish ground with a few hills and not collapse you will be OK. In any case you will toughen up as you go.
Age, fitness, health seem to have little to do with getting Altitude problems or not. In fact you can be fine on one trip, repeat it a year later and have problems, and vice versa. The secret is to take it slow, drink loads of water or tea or hot lemon or similar.
Sensible precautions help avoid stomach problems. Try to keep to "Western" food initially prepared in "Trustworthy" places. Your body has enough with Jetlag, new climate, new lifestyle, introduce new food and drink later on. Take you own insulated mug. Check out
http://www.high-altitude-medicine.com/it has lots of useful info on Altitude, Stomach problems, illness etc
Biggest problem can be getting a cold which you cant shake off and goes to your chest. Take loads of "Lemsip" (OK only Paracetamol, Lemon and sugar but means you are taking lots of fluid). Take cotton hankerchiefs (you can wash them) and bar of disenfectant soap - works much better than liquid soap. Also lots of throat lozenges, first sign of a cold hit it hard and keep hitting it.
Loads of web sites from trekking companies that give equipment lists. Ditto web diaries from people that have made all different treks.
I am not sure about June / July I think this might be into the Monsoon season - check out the forums. The last thing you want is hundreds of photos of clouds behind which are famous mountains (apparently)!
If you have the time and the inclination, think about a Trekking Peak. Something with snow and a real top and a view. As long as the itinerary gives you sufficient time to acclimatise and you are reasonably fit you should be OK. Check out Mera Peak, and there are others. Anyhow once you have got your plastic boots on you will be a few cms taller and your BMI will be fine (as soon as you get on the trail and see some of the other trekkers you will realise that 5Kg is irrelevant).
Have a good time and hopefully you will end up like most of us with an incurable vertical addiction.
Ian