They are not 1.5V cells, but regular Li cells that have a step-down circuit to provide 1.5V for whatever stuff takes that. And anything that needs bursts of high-current won’t work with them (they even warn you about that).
That step-down circuit is likely what’s hosing AM reception.
{Bah, I hit [save] instead of [preview]…)
Anyhoo, they’re not filtered in any way, so all those big fat juicy harmonics will sweep the entire AM band, like you mentioned. Even the output likely has huge ripple currents that can sneak its way through into the radio’s supply. Umm, forget “sneak through”, it’ll use a ram and barge its way into the radio’s supply.
They’re great for things like electric toothbrushes, small lights, anything that’s not critical, but anything that depends on a nice clean supply, forget it.