As far as switching it up...I'm with the overhand or bust thought...its consistently true that most people who can't get 20 pullups yet (including myself) have a better max with an underhand grip. I'd follow the program strictly and on days 1, 3, and 5 do a pyramid of hammer curls followed by curl bar strip downs. This way you're pushing yourself to go with the harder grip while still increasing bicep capacity for which us 'weaker' guys need to get the most underhand pull ups on the test . I do essentially 13 sets of hammer curls starting with 20 lbs dumbbells (warmup). I use hammer curls because they use more of the forearms and biceps area that are used in either type of pull up. I try to get 10 reps (or max)per set except for two max effort sets on the way back down at 25 and 20. I also do three sets at the top of my pyramid to really push myself. So my program looks like this this...20,25,30,35,40,45 x 3, 40... and so on back down doing the two max sets on 25 and 20.
Obviously you use the weight appropriate for your size and strength...but the top sets should not be easy. Following this I do 3 sets of strips downs on a curl bar. Obviously by now your arms are shredded so don't over load the bar. The key to this is to get your biceps through the fatigue...(similiar to what they encounter in attempting a set of underhand pullups)...not lifting heavy weight. It helps to have a workout partner for this. My bar may look like this on one side (10,5,10,5). When you can't do a full rep you take the outside plates off (in this case a 10)...If you're not getting 5 reps on the first lift then reduce your weight...I try to count total reps in each each set mindful that I want at least 20 to simulate pull up fatigue. You can do the empty bar at the end as well, but basically you will have so much blood in your arm that it will be difficult.
One last helpful hint is to not under do it on days 1 and 5...Although I agree that the Armstrong program works well on its own, do some cable rows and lat pull downs after your max effort pullups to further the workout. In my opinion you can never over prepare you upper
body for the stress it will endure and OCS.
Here's the diclaimer...this type of program has been useful to me, but may not be useful to you...I offer these workout additions as a change of pace for those who may be stuck in a rut or want to try something different.
Good luck and good lifting.