Thanks to the kindness of a Japanese acquaintance who procured me a CD-ROM from the homeland, I have a decent bit of shogi software on the computer now. No more freeware from the 90s with an interface to match...
I can now beat the machine on 2-kyu. Some of the computer’s moves were a little opaque to me,  and its tactical ability meant that I had to take back a coupe of moves in order to win this one, but I feel as though I'm improving.
I think that my less-than standard opening move may have caused it to misplace its king in the centre of the board - but that may just be a strategy I'm not aware of. Reading Tony Hosking's excellent The Art of Shogi and Classic Shogi, I can see there's plenty I'm not aware of!
J. vs Computer
1. R68  P34
2. K48  K52
3. S38  G32
4. K39  S62
5. P76  Bx88+
6. Sx88  G72
7. K28  P84
8. P66  N33
9. P46  P85
10. S77  P74
11. B’56  P35
12. Bx76  S42
13. P96  S73
14. B56  S64
15. B78  S55
16. R48  P24
17. P56  S44
18. G(4)58  P25
19. P16  P14
20. P75  G62
21. G79  R72
22. S76  R82
23. G88  P86
24. Px86  Rx86
25. G87  R84
26. P’85  R82
27. N77  P94
28. B67  G61
29. P74  G72
30. S75  P’73
31. Px73+  Gx73
32. P’74  G83
33. P65  P’73
34. Px73+  Gx73
35. P’74  G72
36. P84  P’73
37. Px73+  Gx73
38. P’74  Gx84
39. Sx84  Rx84
40. G’85  R83
41. P’84  R82
42. R49  P’72
43. R79  P’83
44. Px83+  Rx83
45. P’84  R82
46. R89  S31 (luring me forward?)
47. P95  Px95
48. Lx95  P’94
49. Lx94  P’93
50. Lx93+  Nx93 (he has won a lance, but I have lots of pawns in hand)
51. G94  S’92
52. G76  R81
53. P83+  Sx83
54. Gx83  P’88
55. Rx88  K42 (some nasty bishop forks if I’m not careful…)
56. S’82  R51
57. R89  B’98 (see!)
58. R88  Bx76+
59. Bx76  G’66
60. G67  Gx67
61. Bx67  G’66
62. B94  Gx77
63. R86  N’34 (although I am winning, my left-side attack is very congested)
64. G’47  P26 (...and I need to be very careful about my king’s safety)
65. Gx72  Px27+
66. Sx27  P’85 (looks sneaky, but now the computer has no pawn in hand)
67. R89  G78
68. R87  L’26
69. G62  Lx27+
70. Kx27 R41 (if I had a gold in hand it would be mate on the move…)
71. B61+  Rx61
72. Gx61  S’52 (still not enough pieces in hand to trap my king)
73. G62  B’49
74. B’38  Bx38+
75. Kx38  P15
76. Px15  N26
77. K27  G23
78. Kx26  G24
79. R’21  B’98
80. B’51  K41
81. S73+  Bx87+
82. Gx52  K32 (the gold is immune on account of +S62)
83. Rx24+  R’24
84. +Rx24  Nx24 (no need for me to recapture…)
85. N’24  K22
86. G’32  Sx32
87. Nx32+  Kx32
88. B42+  1-0