I currently have H1B status granted last year but I'm locked into working for the company who sponsored me. What is the easiest way for me to achieve a status whereby if I were offered a position with a different employer I could take it without having to wait until the next round of H1B applications and reapplying?
If you are presently in H-1B visa status for Company A, you are NOT "locked into working for this company." Under the H-1B portability rules, you may transfer to another company, say Company B upon USCIS receiving the H-1B petition filed by Company B. It appears that you have another five years on your H-1B remaining since you were counted towards last year's cap. So if a different employer wants to hire you, assuming it is a specialty occupation, you could easily transfer or "port" your H-1B to the new employer and do NOT have to wait for the "next round of H-1B applications."
On a practical note, however, many employer's these days are not sponsoring foreign nationals because of the costs associated with same so I would make sure the new employer is willing able and files the H-1B petition on your behalf before you give notice.
I hope this helps.