Is there ment to be any spring in its pop or is it from factory a lumber-some task to open and close.I suspect the cover has been applied to tight and hope this can be relieved. Yet what is with the adjustments at the base?  

They've produced a series of videos to assist hobbyists in various aspects of maintenance and restoration of '55-'57 'Birds.  Their DVD titled, 'Recovering the soft top'  is part no. CV1 and is priced at $19.95 plus shipping.

Their Internet website is www.classictbird.com

Their FAX number for international orders is 740-622-5151I've always been very satisfied with any purchases I've made from this business and their handling of orders.  Those that I've recommended this business to have always reported that they were happy with their dealing with them as well.

The top on early TBirds are a pain.  They are difficult to handle by one person although it can be done.  There is no spring to pop it, everything has to be done manually.  In putting up the top, I have found that it is better to set the back in place and then do the front.
As far as the your question about the "base", I assume you mean at the back.  Tightness is determined by the two pins that go into the holes in the deck.  They are adjustable, you have to look at them to determine how it is done.  If I remember correctly, there is a set screw which holds them from turning.  You can't get these too tight because you may break the pin that holds the handle to the pins.  It more a feel thing. If your troubles started with the new top, it seems to me the upholsterer is the one to set it right.