The cap-gap does not apply if you are already in H-1B status.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
What do you mean when you say you have 4.5 months of h1 left ? If you we're on h1 b status within the last 6 years the cap does not apply to you and you do not require cap gap.
If you on the other hand the cap applies to you as long as you have valid f1 / opt past April 1 st and your employer files a petition on April 1 st you will be eligible for cap gap.
Please consult an immigration attorney