Hurray!
I think I found the solution. From PayPal's site I found the following page about configuring shipping profiles in PP: https://cms.paypal.com/us/cgi-bin/?cmd=_render-content&content_ID=developer/e_howto_html_ProfileAndTools#id08A9EG0047X
This is the setting I changed: to YES
Use the shipping fee in the transaction instead of my claculator’s settings
Select whether the shipping rates can be overridden by individual transactions if the information is passed to PayPal with HTML variables in the transaction. Allowable values:
Yes
No
IMPORTANT: Changing the setting of a specific shipping method changes the setting for all U.S. domestic and international shipping methods that use the same currency.
Then in wp-eStore I turned off Use PayPal Profile Based Shipping in the settings panel under Payment Gateway Settings.
Then I changed this in eStore_payment_submission.php (comment out the second line): eStore_payment_submission.php:
$myPaypal->addField('shipping_1', $shipping);
//$myPaypal->addField('handling_cart', $shipping);
I put 0.001 in the shipping field of the member button product settings page
Some further testing to be done but looking good.