Here is what Swan 4.0 has to say about handling 1-level interference
Quote
Pass: No wish to compete at the moment or unwilling to commit to game if OP should be strong. Later voluntary actions are balancing, and a later voluntary bid in the suit of an overcall is NAT, NF.
RDBL: General positive, 11+ hp, usually BAL. F-1NT or PEN.
OP passes only with club length, else rebids NAT. 2 is ART FG - also from RP.
1R and DBL of 1R: TRF, at least 4-c M (next suit), 8+ hcp. But if 1R was TRF, promising 5-c relay suit (or 4-c with about 10+ hcp), DBL shows the suit bid.
[...]
1♠ and DBL of 1♠: T/O, denies 4-c suits higher than the overcalled suit. (Over 1, 4-c hearts is possible, and an ART overcalled suit may also be possible as trumps.)
Weak OP usually rebids 1NT (does not promise a stopper), but may choose to rebid 2m with a 5-c suit.
RP’s CUE in OPP’s genuine suit or bid in a suit he has denied asks for a stopper. Otherwise RP’s rebids in m are NF, but rebids in M are F1 with a 4-c suit. RP may bid 1♠ followed by a rebid in clubs in order not to wrong-side NT.
Strong OP rebids something else - e.g. 2NT (2NT methods apply) or CUE (usually BAL without a stopper). A rebid in 2nd hand’s suit is NAT.
1NT/2X: TRF. TRF to a lower-ranking suit may be just competitive. Weak OP may show support by a ”jump” to the 3-level.
If TRF could have been made at the 1-level, a 2-level TRF promises 6-c suit and INV+ values.
Over an INV+ TRF to M, a weak OP bids 2M (NF), 3M (FG, leaving room for slam tries) or 4M (only when single jump after further competition), so new suit (NAT, also in the suit bid by 2nd hand) and 2NT show the strong type.
After TRF to 2X and OP’s 2NT, RP’s bids below 3X are TRF, 3X shows (extra) clubs, and bids above X are NAT. (Exception: RP’s TRF to - or a bid in - the suit of a NAT overcall shows extra values without extra lengths.) RP’s 4m is a ”retransfer” to 4M with MIN but a very good suit.
Over 2♠ (TRF to clubs, INV+), a weak OP bids 2NT (stopper, F1, may also be strong), 3♣ (no stopper, not MAX) or CUE (no stopper, MAX but not FG).
CUE may also be strong without a stopper.
TRF to OPP’s ”genuine” suit (5-c or 4-c with about 10+ hcp) is INV with at least 4-5 in the highest unbid M and a minor. Weak OP may pass 2 or 2, give preference to m by 3 (P/C) or bid NT / RP’s M quantatively. Accept of TRF is ART, either weak OP with game interest or strong. Other rebids are NAT, strong.
TRF to OPP’s ”non-genuine” suit promises that suit.
RP’s rebid in a new suit is NAT F1; raises and bids in NT are NAT INV. A CUE is primarily asking for a stopper; a jump in new suit is SPL.
2NT: 5-5 m. Weak OP bids 3m or 5m (rarely, unless over 4M). A jump to 4m is strong.
3Y: Single jump: INV with good 6-c suit. This includes 3X after ART 1X.
Double jump: Sound PRE with 7-c suit.
3X: (When OPP have shown ”genuine” X): Asking for a stopper, long m.
4m: TRF to 4M (even if OPP’s suit). OP’s relay is strong, and CTL may follow.
OP’s 4NT is RKCB.
RDBL: General positive, 11+ hp, usually BAL. F-1NT or PEN.
OP passes only with club length, else rebids NAT. 2 is ART FG - also from RP.
1R and DBL of 1R: TRF, at least 4-c M (next suit), 8+ hcp. But if 1R was TRF, promising 5-c relay suit (or 4-c with about 10+ hcp), DBL shows the suit bid.
[...]
1♠ and DBL of 1♠: T/O, denies 4-c suits higher than the overcalled suit. (Over 1, 4-c hearts is possible, and an ART overcalled suit may also be possible as trumps.)
Weak OP usually rebids 1NT (does not promise a stopper), but may choose to rebid 2m with a 5-c suit.
RP’s CUE in OPP’s genuine suit or bid in a suit he has denied asks for a stopper. Otherwise RP’s rebids in m are NF, but rebids in M are F1 with a 4-c suit. RP may bid 1♠ followed by a rebid in clubs in order not to wrong-side NT.
Strong OP rebids something else - e.g. 2NT (2NT methods apply) or CUE (usually BAL without a stopper). A rebid in 2nd hand’s suit is NAT.
1NT/2X: TRF. TRF to a lower-ranking suit may be just competitive. Weak OP may show support by a ”jump” to the 3-level.
If TRF could have been made at the 1-level, a 2-level TRF promises 6-c suit and INV+ values.
Over an INV+ TRF to M, a weak OP bids 2M (NF), 3M (FG, leaving room for slam tries) or 4M (only when single jump after further competition), so new suit (NAT, also in the suit bid by 2nd hand) and 2NT show the strong type.
After TRF to 2X and OP’s 2NT, RP’s bids below 3X are TRF, 3X shows (extra) clubs, and bids above X are NAT. (Exception: RP’s TRF to - or a bid in - the suit of a NAT overcall shows extra values without extra lengths.) RP’s 4m is a ”retransfer” to 4M with MIN but a very good suit.
Over 2♠ (TRF to clubs, INV+), a weak OP bids 2NT (stopper, F1, may also be strong), 3♣ (no stopper, not MAX) or CUE (no stopper, MAX but not FG).
CUE may also be strong without a stopper.
TRF to OPP’s ”genuine” suit (5-c or 4-c with about 10+ hcp) is INV with at least 4-5 in the highest unbid M and a minor. Weak OP may pass 2 or 2, give preference to m by 3 (P/C) or bid NT / RP’s M quantatively. Accept of TRF is ART, either weak OP with game interest or strong. Other rebids are NAT, strong.
TRF to OPP’s ”non-genuine” suit promises that suit.
RP’s rebid in a new suit is NAT F1; raises and bids in NT are NAT INV. A CUE is primarily asking for a stopper; a jump in new suit is SPL.
2NT: 5-5 m. Weak OP bids 3m or 5m (rarely, unless over 4M). A jump to 4m is strong.
3Y: Single jump: INV with good 6-c suit. This includes 3X after ART 1X.
Double jump: Sound PRE with 7-c suit.
3X: (When OPP have shown ”genuine” X): Asking for a stopper, long m.
4m: TRF to 4M (even if OPP’s suit). OP’s relay is strong, and CTL may follow.
OP’s 4NT is RKCB.
After reading all that, I'm still not sure whether I'm supposed to pass, double, or bid 2♦ on the hand given above.