The Kings, who collected all of the domestic titles last season when called Kingston, beat Derby 91-79 after gaining a 16-point lead in the closing minutes of the first period.
The Basketball League Ltd, who administrate the First Division, have allowed Guildford to circumvent the cap for their European Clubs' Championship games, but will not allow them to use their full-strength squad in the league.
Miller, a 6ft 6in England and Great Britain international, was injured in Thursday's European win over Kalev Tallinn, and Alton Byrd was due to join him on the sidelines. Then their American guard, Thompkins, strained a knee in the warm-up, so Byrd played.
Derby trailed by only four points five minutes from the interval, but then they ran into a familiar pattern of punishing fast breaks from the Kings which gave Guildford a 48-32 half-time lead.
London Towers, without any Americans this season, won 98-87 at Birmingham. London's trio of England internationals, Joel Moore, with 33pts, and the brothers, Richard and Peter Scantlebury, with 23 and 17, outgunned Bullets' lone American, Derek Rucker, who scored 38 points.Reuse content