The rocking may be 'Dutch Roll', this was common on the 707 and the reason for the ventral fin mods at the back. My understanding it did not eliminate it totally and pushing the flight envelope may exacerbate the inherent instability.

RE the service ceiling issue, checked with some ex 707 drivers her in OZ. For the 300 with the JT3D's it was 36,000. For those with JT3C it was 43,000. The original prototype with JT3's it was 43,000. The JT3D's were introduced to reduce noise and improve fuel burn for long or international flights.

Consensus is that for the JT3D's which were turbofans the most efficient operating altitude was FL330 and FL350 and never above FL370.

Either way at FL360 you hit the tropopause where you loose the benefits of decreasing OAT and the lapse rate changes. It will start to warm as you go higher and you will burn a lot more fuel. Name of the game was to get as high as you could for the maximum TAS for the minimum fuel burn. You need the detailed performance charts to work out the planned level you intend to operate and the forecast temps to get an idea if it is ISA, ISA minus or ISA plus and then look for the level that ives the maximum thrust for least fuel burn.  8-)