I would expect that building mileage would help more for improving your half PR, and doing speed work twice a week would help more for improving your 5K PR.
If you have a copy of Daniels' Running Formula, I might suggest doing the six week phase II & phase III from his 5K/10K plan*, 12 weeks total (you can probably skip phase I if you're already running 30-35 per week). Do this at around you current mileage, maybe increase to 35-40 in phase III, but make sure you're not too worn out to do the workouts.
*If you don't have a copy, Phase II generally consists of one workout of 200's/400's at mile pace (equal distance jog for rest) per week, one tempo workout (1 or 2 mile repeats), and one long run. Phase III replaces the mile pace workout with a 5K pace workout. For your volume, I would recommend something like 8x400 or 4 sets of 200/200/400 for a mile pace workout. Tempo workout might be 4x Mile with a minute walking rest, or 2x2 Mile with 2 minutes rest. 5K workout could be 4x1200 / 3 min jog rest or 6x800 / 2 min rest.
At the end of these 12 weeks, you can try running a 5K time trial, and maybe take the week after a little easier- no workouts, ~30 miles. Then shift gears and work on half marathon fitness- this would mean dropping one of the workouts per week, and just doing a tempo run and long run each week. Make up for the lower intensity with more volume, adding ~5 miles every four weeks. You can try increasing the volume of the tempo workouts to 5 or 6 x Mile, or 3x2 Mile as your total volume goes up, and do a long run of 25-30% of your weekly mileage. Do this four about 12 weeks, half marathon time trial, week easy to recover, and there's six months.
What I like about this is I find track workouts easier during the summer- muscles feel looser, you don't have to worry about snow on the track depending on where you live, whereas longer runs and higher volume feel easier in the fall when there's less chance of overheating. After spending much of the summer working on mile pace and 5K pace, your half marathon pace should feel easier when you shift your focus back to that in the fall.