The reason Svetlana tubes oscillate in the FL2100 is two-fold: 

1. FL2100 Bias is inadequate for Svetlana tubes. Svetlana tubes have LOWER mu (not higher as some people claim) and draw more current for a given amount of bias. 
2. The FL2100 has no neutralization and is not stable at HF under all load conditions. This is true with any tube in this amplifier.

The FL2100Z was revised in an attempt to fix these problems. The FL2100Z:

1. The FL2100Z has an improved (but still unusual) bias system.
2. The FL2100Z has a very poor attempt at neutralization or feedback.

Bias Error

The FL2100 only applies ~15 volts negative bias to the 572B grids for cutoff. This is not adequate for some 572B tubes, especially those with slightly lower mu like Svetlana tubes.

Yaesu obviously learned standby bias was not high enough. Later versions of the FL2100, the FL2100Z, used a voltage tripler in the bias.

An inexpensive 12V low current relay corrects the bias issue with out complicated circuit or wiring changes.

Feedback Error

The FL2100 design uses a capacitor from the OUTPUT of the pi network back to the input of the tubes. A good design would NEVER do something like this. A pi-network  transforms phase along with load impedance. As the tuning and loading controls are moved, and as the antenna load impedance changes, the phase of the feedback voltage changes. The output tuning and loading as well as the antenna impedance greatly affects feedback voltage.

A good design would never neutralize or add feedback from the OUTPUT of a tank circuit with a varying load back to the input.

What the design errors do in the Yaesu FL2100

When the antenna relay open, the LOAD is removed from the pi network. This INCREASES the amount of feedback by several times. The tubes, having less mu and requiring more bias, are no longer in cutoff with the relay open and draw current. This allows the tubes to amplify, and the greatly increased feedback causes the FL2100 to oscillate on whatever frequency the tank is tuned to. With no load, the voltage soars to many kV until the bandswitch arcs.

Changing tube brands in even a reasonably design amplifier is no problem at all. Changing tube brands (especially when a brand does not have the same characteristics) in an amplifier with multiple major design errors can be a big problem.

The Svetlana "fix" of increasing FL2100 bias is really not a " fix". It is a marginal patch.

Corrections

Feedback

The most important "fix" would involve removing the capacitor from the output of the tank back to the tube input. This would disable the very poor feedback system. Neutralization page.

If the amp is unstable at upper HF, a neutralization system similar to that used in the AL-811H or AL-572B Ameritron could be used. 

Bias

The FL2100 bias system should be rewired so the relay opens the filament CT return. Normal operating bias should be left on the grids. This would FULLY cut-off any tube brand.