You could overwrite bootstrap's css inside the tabbed area:
.tab-content>.tab-pane {
display: none;
}
with
.tab-content>.tab-pane {
display: block;
}
Then you could do some CSS/JS trickery to position the other elements absolutely so it does not through off the layout. I am actually having the same exact issue. I saw this post and I think it helped me to solve my problem as well. Thanks and I hope this helps.
My plunkr: http://plnkr.co/edit/tgpyZq3JD1hwxtwCwWv8?p=preview