Getting faster on run/bike - strategy for off season

The number one for me would be to join a gym (or buy the kit yourself) and work on your core strength. Dead lifts, power cleans, squats, kettle bell swings, dumb bell chest press will all work muscles you will be calling on when racing in addition to giving you stability in running and cycling. Try to stick to free weights as these will recruit supporting muscles, rather than using machines.

If you're new to resistance work I'd join a gym and get some instruction. And, I'd work up the weights slowly rather than diving in with heavy weights otherwise you risk injury.

I'll change what Danno said slightly.  Run more often and bike harder.

Google BarryP running plan.  Can you dedicate 4 hours a week spreading the time over 6 days of running?  Then add 10% to the total time each week?

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Were I you, I'd strive for consistency.  Running more often, as some mentioned, will help get the body more comfortable with running. This will help you speed up a bit.  Note that "more often" may not mean more mileage.

Someone mentioned going harder on the bike.  What I have found very helpful in this regard is two different items.  One has been to add intervals to my solo rides.  There is no need for fancy equipment, just a willingness to ride hard to the next telephone pole, or street corner, or the county line.  Do it more often during rides, with less rest/recovery between intervals. Number 2 is that riding in a group has pushed me . I often ride with the stronger group and I may not be able to keep up for the whole ride, but each time out I get dropped later in the ride.  I take that as a win. If you have a Local Bike Store that does group rides, or a local bike club, you may be able to hook up with some of their group rides.  The challenge looks like your schedule and group riding may not work together.  

All of these runs will be zone 1 and 2.  Since I focus on 70.3s, I will repeat weeks 8, 9 & 10 until I get about 12 weeks out from my first race.  Then I will will throw in a tempo run for one of those medium runs. When I'm 6 weeks out from a race, I will throw in tempo\speed work for the other medium run.

I look at 2 a days as a morning/night commitment, not a bric. Today was an EZ 30 minute run this morning and I'll do an hour on the bike after work. Some of that hour will be dedicated to intervals.  My reasoning is that the time running is time well spent.  The time biking is time spent improving bike abilities. To the OP's point of time constraints, this may not work.

One of the other aspects that someone here stressed to me a long time ago is to have a purpose to each workout. That doesn't mean every workout has to be fast/hard/intense.  To the contrary, it may simply be recovery or an EZ day to work on another aspect like form.  But you should know what and why to a certain degree. Also, if I am on a 3s/3b/3r cycle, then I'll have 3 double days, 3 single days and a rest day. 

I thought the group ride option was not for you, but I figured I throw it out there anyway. 

One other aspect of this that has struck me lately is how much easier it is in year 4 than it was in year 1.  I attribute that to base building, repitition, and a bit of consistency.  It took me a couple years to figure out what my body is telling me.  And I am starting to get comfortable with pushing myself more.  All that. combined with more knowledge in general and I'm finally beginning to make some headway on a few things.  I admit, I have taken a while to figure stuff out, hopefully you are a bit quicker on the uptake.  I'll never be fast, as that is not my sole objective, but I will be faster.  For me, the fun matters.  

Enjoy it all as much as you can!

I do all my weekday rides on a trainer.  I will ride an hour on the 3 short rides and do a long ride outdoors  (2-3 hours) on the weekend.  I swim on the medium run days.  Closer to race day, I will start doing tempo and speed work.