Update several fields in thousands rows - sql-server

Question

I have database MS SQL Server 2008 R2 with loading 2000 transactions per second. Tables are:
'lion_Tasks'(uid_obj, order_new, __usn_field_order_new, and more 40 fields)
and
'lion_Tasks_Changes_Parts'(uid_task_cp, uid_user_cp, __usn_entity_cp and more 20 fields )
Web-server get 10.000 objects, in which only one field has changed 'order_new'. Only 3 fields need to be updated in the database. These objects I pass in a table parameter to the stored procedure:
I tried to rewrite this stored procedure several times without any performance changes, it still trips out 10-20 seconds, current version is:
CREATE PROCEDURE dbo.lion_UpdateTasksNewOrder
( #Table TasksNewOrderTableType READONLY)
WITH RECOMPILE AS
BEGIN
DECLARE #ErrorCode int
SET #ErrorCode = -1
UPDATE TasksTable
SET
order_new = t.ORDER_NEW,
__usn_field_order_new = t.USN_ORDER_NEW
FROM dbo.lion_Tasks TasksTable
INNER JOIN #Table t
ON t.UUID_TASK = TasksTable.uid_obj
IF( ##ERROR != 0 )
BEGIN
SET #ErrorCode = -1
GOTO Cleanup
END
UPDATE TasksTableCP
SET
__usn_entity_cp = tcp.USN_ENTITY
FROM dbo.lion_Tasks_Changes_Parts TasksTableCP
INNER JOIN #Table tcp
ON tcp.UUID_TASK = TasksTableCP.uid_task_cp AND tcp.UUID_USER = TasksTableCP.uid_user_cp
IF( ##ERROR != 0 )
BEGIN
SET #ErrorCode = -1
GOTO Cleanup
END
RETURN 0
Cleanup:
RETURN #ErrorCode
END
The temp-database is located on the SSD disk. Maybe someone tell me what to do for acceleration?
The estimated execution plan is:
https://www.brentozar.com/pastetheplan/?id=Byq2JzTwm
Table script:
USE [lion_data]
GO
/****** Object: Table [dbo].[lion_Tasks_Changes_Parts] Script Date: 09/05/2018 11:31:53 ******/
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
CREATE TABLE [dbo].[lion_Tasks_Changes_Parts](
[uid_obj_cp] [uniqueidentifier] NOT NULL,
[uid_task_cp] [uniqueidentifier] NOT NULL,
[uid_user_cp] [uniqueidentifier] NOT NULL,
[_order_cp] [int] NOT NULL,
[uid_marker_cp] [uniqueidentifier] NOT NULL,
[date_begin_cp] [datetime] NULL,
[date_end_cp] [datetime] NULL,
[readed_cp] [int] NOT NULL,
[collapsed_cp] [int] NOT NULL,
[__usn_entity_cp] [int] NOT NULL,
[__usn_field_order_cp] [int] NOT NULL,
[__usn_field_uid_marker_cp] [int] NOT NULL,
[__usn_field_date_begin_cp] [int] NOT NULL,
[__usn_field_date_end_cp] [int] NOT NULL,
[__usn_field_readed_cp] [int] NOT NULL,
[__usn_field_collapsed_cp] [int] NOT NULL,
[__usn_field_list_tags_cp] [int] NULL,
[Contacts] [nvarchar](max) NULL,
[__usn_field_contacts_cp] [int] NULL,
[uid_user_marker] [uniqueidentifier] NULL,
[__usn_field_uid_user_marker] [int] NULL,
[focus_cp] [int] NULL,
[__usn_field_focus_cp] [int] NULL,
CONSTRAINT [PK_lion_Tasks_Changes_Parts] PRIMARY KEY CLUSTERED
(
[uid_obj_cp] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY]
GO
Scripts for indexes:
USE [lion_data]
GO
/****** Object: Index [PK_lion_Tasks] Script Date: 09/05/2018 11:28:44 ******/
ALTER TABLE [dbo].[lion_Tasks] ADD CONSTRAINT [PK_lion_Tasks] PRIMARY KEY CLUSTERED
(
[uid_obj] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, SORT_IN_TEMPDB = OFF, IGNORE_DUP_KEY = OFF, ONLINE = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
GO
USE [lion_data]
GO
/****** Object: Index [IX_lion_Tasks_CP_Uid_Task] Script Date: 09/05/2018 11:29:17 ******/
CREATE NONCLUSTERED INDEX [IX_lion_Tasks_CP_Uid_Task] ON [dbo].[lion_Tasks_Changes_Parts]
(
[uid_task_cp] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, SORT_IN_TEMPDB = OFF, IGNORE_DUP_KEY = OFF, DROP_EXISTING = OFF, ONLINE = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
GO
USE [lion_data]
GO
/****** Object: Index [IX_lion_Tasks_CP_Uid_User] Script Date: 09/05/2018 11:29:30 ******/
CREATE NONCLUSTERED INDEX [IX_lion_Tasks_CP_Uid_User] ON [dbo].[lion_Tasks_Changes_Parts]
(
[uid_user_cp] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, SORT_IN_TEMPDB = OFF, IGNORE_DUP_KEY = OFF, DROP_EXISTING = OFF, ONLINE = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
GO