Why will these steps NOT fix the problems with LIBOR?
Rather than answer regarding your specific proposal, as that would be of less use generally than providing the current state of thought about interest rate benchmarks, I will provide a quick review of the literature, allowing you to think more generally about the issue. 

Regarding LIBOR specifically, the Wheatley Review of LIBOR was the foundational document outlining the general issues with LIBOR and setting a path for reform. After this review, the International Organization of Securities Commissions (IOSCO) published a report, "Principles for Financial Benchmarks" that addresses general issues surrounding benchmark governance, quality, methodology, and accountability. You will find that this report is particularly important in thinking about benchmark calculation approaches, as it provides a framework for evaluation of benchmark proposals, yours included.

Since then, the Financial Stability Board's Official Sector Steering Group has issued specific recommendations relating to LIBOR reform; this document relates the general IOSCO principles to the specific issues that arise in interest rate benchmarks.

Finally, two academic articles may prove of interest to you. 

Duffie and Dworczak's "Robust Benchmark Design" discusses the design of robust estimators in situations where a benchmark is based on transactions and agents attempt to manipulate these transactions to profit on derivatives based on the benchmark. 

Finally, Duffie and Stein discuss LIBOR reform and alternative reference rates in "Reforming LIBOR and Other Financial-Market Benchmarks."