I would discourage this thought for two reasons: 1) The nose gear door prevents exhaust heat damage and carbonmonoxide from enterting the tunnel (if you used the forward close out piece attached to the strut) and possibly into the cockpit.  2)  The aerodynamic affects may be significantly detrimental.

What are the real issues causing the headaches?  The listers here will be able to provide you with solutions and photos etc to help you solve the problems.

Larry Henney