Depending on your cooking method you shouldn't have any problem with the joint drying out. By it's very nature, a joint contains a lot of connective tissue. That connective tissue will gelatinize under a slow roast and make the meat come out extremely juicy. The best way to do this is going to be a lot of low dry heat (like the kind you get in your oven thats set to about 200-250*F). You could also slow cook it, as in a crock pot, but only if you don't want slices. BTW, if you want a crust on that bad boy, just kick your oven up to five hundred when the roast gets to about ten degrees from where you want it, and it should crust up nicely.
Finally, don't forget that all large pieces of meat are going to keep cooking even after you remove them from the heat so make sure that you take that into consideration when deciding what temp to yank it out at.
The only mistake you made was the choice of cut, and maybe the quality of the beef itself. Round (in the UK/AU/NZ topside and silverside) is from the rear end of the animal, and is a working cut. Working cuts have to exert a force, so the muscle must have lots of collagen to distribute the force from the tendon throughout the muscle. Collagen is a tough material which breaks down in the presence of heat and moisture, not just heat, so working cuts make poor roasts or steaks and are better braised or stewed.
The upside to working cuts is that they have a stronger flavor, and the collagen when broken down by moisture turns to gelatin which adds to the flavor and mouth feel. A well-prepared braised piece of beef is as good as a roast any day in my opinion. It's also better value, round and other working cuts are much cheaper than tender cuts.
Your technique as described is perfect, and if you'd chosen a rib, short loin, or sirloin roast (US cuts) it would have come out beautifully. Where you erred was at the store when you chose a working cut for roasting.
Now some people on the forum are probably preparing a rebuttal at this point saying "you can roast round and have it be tender", and they'd be right up to a point. The best quality beef is reared and slaughtered better, so if you bought US Prime round it has a good chance of coming out relatively tender, however it's hard to find. My assessment would be for what you'd find in the average store in the US, which is Choice grade. Choice encompasses something like 75% of beef produced, so has a huge range of quality.
You can tell a lot about meat by touching it. Stick your fingers in it, if they go in easy and the meat springs back then you have a tender cut, if you can't get your fingers in it it's a braising cut. If you stick your fingers in and the meat doesn't spring back its old, so don't buy it.
Best Answer
Meat is tough for two reasons:
1- An abundance of connective tissue.
2- When over cooked.
In your case I'd say you probably have both problems. Cheap meat is tough meat. It is from older animals or well worked muscle groups. This means that it has been fortified with a lot of extra connective tissue. It also means it has a lot of flavor.
The solution to #1 is slow, wet cooking that will melt that connective tissue into delicious gelatin. Braising is the normal way to do this. When meat is heated too far, even if the connective tissue has been carefully melted out, the meat proteins bunch up and stiffen- resulting in #2, a dry, unpleasant meal.
You are buying tough meat and cooking it relatively quickly with no thermometer. You don't have enough time or moisture to melt the collagen and you can't be sure you haven't over cooked the meat because you don't know the temperature. Using time doesn't work because chunks of meat are irregularly shaped so you can't know how long it will take for the heat to penetrate.
Buy yourself a probe thermometer to prevent #2. For #1 look for pot roast recipes. Some are easily done in slow cookers- others use a tent of sealed foil over the meat to seal in moisture. Plan on it taking much longer than your 1.5 hours. 3-6 hours are typical to produce a really succulent pot roast.
The searing is just for flavor and will not play a role in either melting collagen or cooking the interior of the meat.