OPT结束后的工作签证时间线？

刚刚从旧雇主辞职，在和新雇主讨论可能的签证情况，新雇主(某University)愿意支持签证，表示越快入职越好，最迟10月。正在和律师沟通，但也请问一下各位朋友的建议。或者，有最近申请工签的朋友能分享一下timeline吗？非常感谢你的阅读和回答！



Status:

• F-1 (program end 22/6/10), STEM-OPT (expires 25/6/30), no unemployment date so far for OPT, STEM-OPT periods (22/7-25/6)
  
• Have petitioned EB2-NIW (11/24), I-140
  
• Received a J-1 advisory opinion at 25/3, stating subject to 212E rule because of Gov. funding (although on DS-2019 it states that No Gov. funding)

Potential Options (Other options?):

• Submit J1 wavier immediately, and at the same time apply for H1B visa
• Submit an O1 visa (can I use my EB2 attorney, Wegreened, for this purpose?) My reading is that one has to have a consular processing for this.
• Apply for a next J1 visa if the University agrees to it.