Think of it like this...
In music school they say off the bat you MUST be practicing at least 21 hours a week - which matches up with your 3 hours a day. This, however, is a long term plan (for 4 years of practice). If you have a year + to study for the LSAT, 21 hours a week shouldn't be all that bad. I have personally found 4-6 hours a day to be ideal for my improvement. If you are trying to get into the high 160s within 3 months - try 30+ hours a week. My goal is the low 170s - which may take 6 months+ at 30 hours a week for me.
If you are serious about the LSAT and law school, structure you day so that you can squeeze in as much efficient LSAT study as possible. Even on days you can't get a whole lot in still keep your mind on LSAT. Read through sections you have done, review methodology - question types, etc. Read online resources about the LSAT, like this forum. Keeping your mind on the LSAT is just as important as studying for it. A day shouldn't go by without you at least looking at something LSAT related.
One more thing - taking the diagnostic test is fine but make sure from here on out you focus only under un-timed conditions. Once you have a firm grasp of fundamentals (once you can answer all the questions correctly un-timed) then move on to timed tests. Why? If you can't answer the questions un-timed - theres no way you will be able to answer them timed. Once you can score in the 175+ range on an un-timed test - then move on to time management. Make sure that you are learning an efficient method (which all of the major prep companies have) so you can bring your time down when it is relevant. You will also notice, however, that once you have a firm grasp on fundamentals, timing should become less of an issue. Remember, its not speed but efficiency.