Desk-pilot:
Pension investment management is nowhere near as straightforward as you assume. For a start, the fund is not only trying to find investment returns, but has obligations to pay out to those who are current pensioners. If fully invested in property, you would find yourself with illiquid investments in property funds, and be totally unable to pay the obligations to your present pensioners.
I do not know how you come to the conclusion that the deficit is solely the result of the investment performance. Granted, there are some good and some bad managers in which the fund will be invested, but for a fund the size of NAPS, it is wholly unrealistic to expect that the fund can be entirely invested in the best managers (as their fund sizes are capped, and good managers are often only shown to be so after the event). Furthermore, the deficit arises not only through investment performance, but also through the present valuation of the liabilities, and hence changing age assumptions and discount rates of gilts have huge effects on the valuations.
It is wholly foolish to invest a fund the size of NAPS in property to any greater degree than around 10% (including all other alternative assets). Productive investments in companies are far better investments that depend not only on the sale of the asset, but generate significant operating returns in the interim (something that property assets often fail to achive through rentals).
This thread is not a discourse on investment strategy, but comment is required to rectify misconceptions.
I would also hesitate to speculate as to the impact of whatever BA plan, since there are many options and alternatives, depending upon the involvement of the regulator and the legal structure of the fund.