Many of my favorite recorded performances of Beethovens symphonies are by conductors who never recorded the whole cycle.
Ill limit myself to mentioning only one: Carlos Kleiber. His recordings of the 5th & 7th symphonies, Vienna Philharmonic (DGG), are stupendous. He recorded the 4th live with the Bavarian Radio Orchestra (Orfeo, may be hard to find) and it is also a trully great performance.
The Solti/Chicago (I do agree that the London LPs sound better than the CDs) and Karajan/Berlin (the cycle from the 70s, DGG) are, for me, the most satisfying complete modern cycles. Conductor, Wilhem Furtwangler (with various orchestras), is one of my favorites of the old guard for his personal and unique way with these works, but you'll have to settle for (sometimes) less-than satisfactory sound reproduction. Really a small price to pay for what you receive emotionally.
An interesting, and totally outrageous view of the symphonies by Roger Norrington (Angel) was recorded during the musicologically-correct epoch of the 1980s & 90s, when cats ran for their lives to avoid having their digestive plumbing used for violin strings. I still own it on LPsit was issued also on CDsand merits a hearing now-and-then for the panache and lack of religious reverence that, many times, afflicts performances of these works.
There are even complete cycles by pianists (the Liszt transcriptions). A recording of the 5th symphony by Glenn Gould is quite good.
Anyway, good luck with your search and best wishes.