Late twenties and fairly clueless. What should we be doing?

Right-oh, so the situation we're currently at is as follows:

We're yet to exchange on the house and there's a sizeable building regs sticking point in the way. We have opened one S&S ISA with a meagre monthly direct debit to be reevaluated once we have completed on a house and are in position to plan with more clarity. These are currently invested in Vanguard LifeStrategy 80% while I read and digest online blogs (e.g. Monevator) and the two books I've got hold of on the subject (Smarter Investing by Tim Hale and Ivesting Demystified by Lars Kroijer).

Obviously, the most financially sound investment we could make is to increase our contributions to our DB pension schemes (TPS and NHS) but we could not access these guarantee due returns until NPA; the hefty actuarial reductions make me wince. Whilst the majority of both sets of our relatives have lived into their eighties and nineties, I'm not convinced that we would be fit enough to benefit from enhanced pensions after the age of 68. So the core purpose of our investments is to 'fund the gap' between early retirement and our DB benefits kicking in at NPA (which is currently 68 for us) although we may both have small sums coming in from 65 from a few years of contributions to pre-2015 Final Salary schemes). 60 is a reasonable target for early retirement since, as we were born in the late 1980s, we are planning to expect our NPA to rise to around 70. As such, we need to work out an acceptable balance between buying additional pension through our DB schemes and investing to fund the gap of early retirement.

Now, S&S ISAs may yet form a backbone of our early retirement saving. But SIPPs and LISAs are a more efficient (yet less flexible) way to save for our retire-around-60 goal. For me, it appears as though a SIPP should be the logical wrapper since - unless I achieve secondary school headship - I shouldn't hit LTA. To provide context, the career move I'm hoping to make in the next year to assistant headship typically pays £50-55k pa and an eventual aim to deputy head typically rewards £60-65k pa. As a GP, my wife will earn greater sums than these (once she fully qualifies from March 2018) even working part-time. As such, additional contributions to her DB pension may take her closer to the LTA. This means that we need to consider maxing out her S&S LISA allowance to fund her going earlier than NPA with any excess going into the ISA(s) - as opposed to a SIPP. Are there any spreadsheets around for us to play with?

Also, we do still have short term savings goals. Our cars are both approaching ten years and 100,000 miles - a small SEAT and a smaller Fiat that may not have much longevity. Also, there are homemade improvements to make on the house that we're buying and perhaps most onerously, 'family planning'. We do not wish to buy cars etc 'on finance'. As such, we will be shovelling money into regular savers accounts once we have (re)established our emergency fund of 4 months of outgoings. We will probably also make relatively small overpayments on our mortgage since there aren't no any easy access accounts paying out 2.49+% interest - the rate we hope to pay on our five year fix. We would like to be mortgage-free by 55 yet anticipate one or two (probably two) moves up the ladder to come.

Have we missed anything obvious?