Dondk,
121.343 actually deals with flight recorders. I believe you are referring to 121.434(g), which requires knowledge consolidation within 120 days.
There are several exceptions to this requirement, however. Grandfather clauses were introduced to recognize those who have prior experience in type before 1995. In your case, the company may extend the 120 day period to 150 days if you continue to meet the other requirements for knowledge and consolidation, and if you have complete refresher training before the 120 days expire.
Aside from that, the FAA may grant exception, but only under unusual circumstances, such as difficulties encountered by a start-up operation, or a new domicile.
You may also substitute one takeoff and landing for one hour of required operational experience, up to 50% of the total experience, except for Group II initial and transition training. This relief is provided for in 121.434(f).
If you reach 120 days, you must undergo a proficiency check. 121.434(g) provides that the 120 day period must proceed either any of the flight maneuvers for an ATP/type practical test, or a proficiency check conducted under 121.441. If you can get refresher training prior to that date, you can go for the extension (from 120 days to 150 days), and hopefully complete your consolidation in that time period. The refresher training will be fastest and probably cheapest for the company, but this close, they should be doing everything in their power to get you the hours and experience and get you done.
The proficiency check in this case may suffice as a limited one, as provided in 121.441(d):
d) A person giving a proficiency check may, in his discretion, waive any of the maneuvers or procedures for which a specific waiver authority is set forth in Appendix F to this part if -
(1) The Administrator has not specifically required the particular maneuver or procedure to be performed;
(2) The pilot being checked is, at the time of the check, employed by a certificate holder as a pilot; and
(3) The pilot being checked is currently qualified for operations under this part in the particular type airplane and flight crewmember position or has, within the preceding six calendar months, satisfactorily completed an approved training program for the particular type airplane.
As Bayoubandid said, get with your training department (via channels, as appropriate) and follow up on this before it grounds you or causes you other headaches.