Consider using Parliament Act
I seem to recall Blair controversially and unjustifiably using the Parliament Act to force through anti fox hunting legislation.
As I recall, the Parliament Act is for those occasions when the Lords persist in blocking government policy.
The Commons voted with a majority to grant us a referendum on Brexit. A majority voted for Brexit. The government is working to achieve it. The Lords are working to thwart the will of the people and the Commons. The Parliament Act is there for just such a situation.
So why doesn't May invoke the act for all Brexit legislation and then again to get rid of the Lords?