Need approval of transformer driver design
Following is your schematic (sans the transformer secondary) and its circuit list generated with LTspice, the circuit list included so you can simulate/troubleshoot the circuit yourself and find whatever errors may be lurking there just waiting to head you off at the pass. ;)

If you don't have LTspice it's available, free, here: 



Version 4
SHEET 1 880 1048
WIRE -384 -256 -624 -256
WIRE -32 -256 -384 -256
WIRE 96 -256 -32 -256
WIRE 416 -256 96 -256
WIRE 576 -256 416 -256
WIRE -384 -208 -384 -256
WIRE 416 -144 416 -256
WIRE -384 -96 -384 -128
WIRE -384 -96 -448 -96
WIRE -32 -96 -32 -256
WIRE 352 -96 288 -96
WIRE -384 -64 -384 -96
WIRE -96 -48 -208 -48
WIRE 288 0 288 -96
WIRE 288 0 -32 0
WIRE 416 0 416 -48
WIRE 688 0 416 0
WIRE -208 32 -208 -48
WIRE 416 48 416 0
WIRE -384 80 -384 16
WIRE -272 80 -384 80
WIRE 288 96 288 0
WIRE 352 96 288 96
WIRE -384 144 -384 80
WIRE 576 192 576 -256
WIRE 688 192 688 0
WIRE 416 208 416 144
WIRE 416 272 576 192
WIRE 576 272 416 208
WIRE -384 288 -384 208
WIRE -32 288 -32 0
WIRE -32 288 -384 288
WIRE 416 336 416 272
WIRE 352 384 288 384
WIRE 96 480 96 -256
WIRE 288 480 288 384
WIRE 288 480 96 480
WIRE 416 480 416 432
WIRE 688 480 688 272
WIRE 688 480 416 480
WIRE 416 528 416 480
WIRE 96 576 96 480
WIRE 288 576 288 480
WIRE 352 576 288 576
WIRE -624 624 -624 -256
WIRE -32 624 -32 288
WIRE 32 624 -32 624
WIRE -624 784 -624 704
WIRE -448 784 -448 -96
WIRE -448 784 -624 784
WIRE -208 784 -208 128
WIRE -208 784 -448 784
WIRE 96 784 96 672
WIRE 96 784 -208 784
WIRE 416 784 416 624
WIRE 416 784 96 784
WIRE 576 784 576 272
WIRE 576 784 416 784
WIRE -624 864 -624 784
FLAG -624 864 0
SYMBOL npn 352 -144 R0
SYMATTR InstName Q4
SYMATTR Value 2N2222
SYMBOL npn 352 336 R0
SYMATTR InstName Q6
SYMATTR Value 2N2222
SYMBOL npn 32 576 R0
SYMATTR InstName Q3
SYMATTR Value 2N2222
SYMBOL npn -272 32 R0
SYMATTR InstName Q1
SYMATTR Value 2N2222
SYMBOL pnp -96 0 M180
WINDOW 0 63 67 Left 2
WINDOW 3 59 31 Left 2
SYMATTR InstName Q2
SYMATTR Value 2N2907
SYMBOL res -400 -224 R0
SYMATTR InstName R1
SYMATTR Value 10k
SYMBOL cap -400 144 R0
SYMATTR InstName C1
SYMATTR Value 10n
SYMBOL ind 672 176 R0
SYMATTR InstName L1
SYMATTR Value .1
SYMBOL res -400 -80 R0
SYMATTR InstName R2
SYMATTR Value 1000
SYMBOL Misc\\battery -624 608 R0
WINDOW 0 9 99 Left 2
WINDOW 3 10 12 Left 2
WINDOW 123 0 0 Left 2
WINDOW 39 0 0 Left 2
SYMATTR InstName V2
SYMATTR Value 6V
SYMBOL pnp 352 144 M180
WINDOW 0 63 67 Left 2
WINDOW 3 59 31 Left 2
SYMATTR InstName Q5
SYMATTR Value 2N2907
SYMBOL pnp 352 624 M180
WINDOW 0 63 67 Left 2
WINDOW 3 59 31 Left 2
SYMATTR InstName Q7
SYMATTR Value 2N2907
TEXT -608 816 Left 2 !.tran ,1