I have the same problem, though not quite as bad, have you upgraded your battery yet? I just got a 200A alternator off Amazon for $118. Hasent arrived yet, but I'll let you know after I have it installed also got some 0ga wire to upgrade the power and grnd connections.

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1999 2.5L Ranger with Kenwood x498 deck, (2) 12" Kenwood shallow mount subs on a Kicker 1000w RMS amp. (4) 5x7 door speakers on 2ch 200 watt RMS amp. 200A alt, AGM battery, Big 3+, and 1/0 wiring. Turn signal mod, throttle pedal mod, air box mod and custom grill inserts.