I am thinking spray foam on the outside of the logs.
I like your basic idea of furring out and adding foam, but rigid foam will allow too many gaps and too much air flow between the rigid foam boards and the very uneven surface of the logs. Those air gaps will greatly reduce the effectiveness of the insulation.
Go with closed cell foam
Spray foam on the other hand will fill all of those gaps beautifully. It will truly encase the home in insulation and perform really well.
Though expensive, I would go with closed cell foam. It will get you a higher R Value than open cell foam, it will provide better moisture control and still move a bit when it needs to as the logs expand and or contract slightly as all wood does.
Cover with the siding of your choice
So, I would say fur out around the house with maybe 2x4's and then have an insulation company come and blow closed cell foam against the house - approx. 3" thick (R value of about R21).
Then put on the siding of your choice. The 2x4's (being truly about 3.5" deep) will allow an airspace naturally to occur behind the new siding (because the foam is only 3" thick). This is ideal. You definitely want the air space behind the new siding.
You will have a basic 'rain screen' at this point. Great!
Insulating other areas
While the foam guys are there I would have them address what they can in the basement or crawl space and in the attic as well.
I would use open cell foam or another sort of blow in (like cellulose) if you are insulating the attic floor. It is significantly less expensive.
If, however you are insulating the underside of the roof, go with the closed cell.
For more information:
Read "Can I improve the energy efficiency of my log cabin by adding foam insulation and drywall to the inside of exterior walls?" a Q&A answered by Polly Osborne.