Adding a flag to bandpopup / bandbox to force bandpopup follow the bandbox width.
A possible implementation could be in bandbox:_fixsz(...)

It could be possible to add a flag check such as:
_fixsz: function (ppofs) {
var pp = this.getPopupNode_();
if (!pp) return;

var pp2 = this.getPopupNode_(true);
if (ppofs[1] == 'auto' && pp.offsetHeight > 350)

{ pp.style.height = '350px'; }

else if (pp.offsetHeight < 10)

{ pp.style.height = '10px'; if (this._shadow) this._shadow.sync(); }

if (ppofs[0] == 'auto') {
var cb = this.$n();
if (pp.offsetWidth <= cb.offsetWidth)

{ pp.style.width = zk(pp).revisedWidth(cb.offsetWidth) + 'px'; if (pp2) pp2.style.width = '100%'; }

else

{ var wd = jq.innerWidth() - 20; if (wd < cb.offsetWidth) wd = cb.offsetWidth; if (pp.offsetWidth > wd) pp.style.width = wd; }

}

if(this._fitPopupToBandbox)

{ var cb = this.$n(); var wd = cb.offsetWidth; pp.style.width = wd+"px"; }

}

so that if the bandbox is declared:
<bandbox fitPopupToBandbox ...></bandbox>
the popup size will be calculated to match the bandbox input size.

See attached example for the desired result