You need to commit. Don't even contemplate failure, as soon as you doubt yourself you increase your chances of blowing the wave. You're probably not surfing waves so big as to harm you so take a few wipeouts, it'll help you realise they're not so bad (apart from the cold). Just cover your head, curl up and relax to save oxygen.
Different locations and swells make different waves and the take off won't always be the same. You're only mortal and sometimes you need to take a few wipeouts just to work out how to tune yourself into the conditions. Don't let it phase you if you don't make your first few waves. Wiping out is better than not catching waves. No one likes to see people pull back from a wave after intimating they are going for it. That will only be accepted a few times before you start getting dropped in on.
With regards to actually taking off under the lip. Sounds like you know the answer, the moments hesitation is costing you valuable paddle strokes to get into the wave early enough. Get your head down and paddle hard. Getting your noggin down will weight the front of the board more helping you get into the wave earlier (and also pearl). Once you feel the wave take you get your hands flat near the rails and chest up (cobra), stall your decent down the wave by leaning back, look down the line wear you want to go and get to your feet. Depending on how fast the wave is this all happens equally as fast. When your learning it all happens way too fast and water time is the only way to get it all dialled and keep it so. So you need to take those wipeouts, not back down and convince yourself you are gonna make the wave. And even then your never gonna get every wave right. Surfing is 99.9% mental (that's full of shit but just sounded good to end on).
Anyway, all I really wanted to write was... have a look at Slater's 1st wave vs. Adriano http://www.oneill.com/cwc/?page_id=2569
in Round 5. Look how Adriano takes off trying to hustle KS off the wave. And at Peniche in Round 5 Fanning had a drop where he was above the lip as it barrelled below him, stood up half wave down as he landed just after the lip. Nuts.