They're the basis of most of hammets leads and alot of earlier 70's/80's rock yet my speed with them is severely holding me back.

Examples of such are:
Ozzy Osbourne - Perry Mason

ending of solo -
e ----15-13-10-----------15-13-10-------
b -------------13-10-13-----------13-10-13

e ---16-15-13-----------16-15-13-------------
b -------------15-13-15------------15-13-15--

e - 17-15-13----------13b
b - ----------12-13b--13b


or off no more tears:

..............................x2.............................x2.
e -13-10-13-10---------15-13--15-13---------17-15-17-15-------
b --------------13-10-----------------15-13---------------18-15-

........................................x2...
e - 18-15-13----18-15-13-------20-17-15----20-17-15----20b
b -----------15-----------15-------------17-----------17


the only way i can pull it off to get the right speed is to do a trill by making my right hand all rigid.

Is there a way to pull it off without playing it as a trill? With just regular alt picking?

thanks